you welcome everybody i’m darren Starnes and i am currently sitting in my classroom at the Lawrenceville school having just enjoyed our very first truly spring day and 75 degree weather and this is Josh I’m sitting in my house in Tucson Arizona having just enjoyed my first summerlike day about 90 95 degrees here in Tucson and we’re really glad that you’re joining us we understand there may be a few students on board so I wondered if we could test out this software those of you that have students watching would you mind just raising your hand there’s a little hand icon next to a checkmark they’re just curious to see what we’ve got out there in terms of didn’t we’ve done it we’ve got a few clicks out there great well welcome to everyone we’re going to jump right in and I’m going to turn off my camera so that we don’t get any kind of interference with the PowerPoint as Nicole said we’ll stop for some questions when we get through the first five tips and then we’ll take questions again at the end so feel free to type those in so our title today is the top ten tips for excelling on the AP statistics exam both Josh and I have been heavily involved in the grading of the exam for quite a few years now and read most recently we’ve been leading individual questions on the exam as they’ve been scored so I’m going to start off with number 10 one of the most important things that you have to realize in statistics that you’re speaking a very special language so my first tip is for the students you got to talk to talk on this exam and by that I mean you have to use the language of statistics very carefully very precisely the AP exam readers are required in most of the rubrics to deduct credit for any misuse of a term so if you’re using any of the terms that are defined in your textbook or on the AP statistics syllabus you need to use them correctly here are a few examples a number of students tend to throw around words like confounding or or biased or skewed in more everyday language but they don’t mean them in their technical statistical sense when the reader sees those words they’re trained to read them exactly as as they’re written so another couple of examples have to do with distinguishing blocking and experiments from stratified sampling I know we’ve both seen those terms used interchangeably when they shouldn’t be and being very careful with use of the word normal a normal distribution is very special bellshaped curve that has some nice properties but in many cases the problem really just requires students to think about whether the distribution they’re talking about is approximately normal so it’s important to get across the ideas that you want to share as a student in your own words more so then you guys you weren’t you interested there you okay we have a couple people not muted they’re in the filling up the other thing that you besides the language is your use of notation so when you are using symbols you have to use those correctly do a couple of common examples when students are talking about means sometimes they unfortunately use the notation like P or P hat which really means they’re talking about a proportion or another common example is using mu instead of xbar or vice versa so it’s really important to be confident about the symbols that you’re using now the formula sheet provides correct symbols for the mean and for the proportion but sometimes it’s easier just to write meam when you want to clarify that you mean mean guard vice and summarizing you got to talk to talk first of all make sure you’re comfortable with the vocabulary and with the notation that you don’t have to worry about these things you can use them like a really well trained statistician and the other is only to use terms and symbols you know it’s better to explain in your own words than to use a term or a symbol incorrectly that’s tip number 10 you got to talk to talk Josh over you I think we got one more on the advice is that apparently we have one more on the advice so when you’re showing work we recommend that you start with the numbers substituted into the formulas we don’t recommend showing the symbolic formula with things like P hat and X bar and use of P hat because it’s way too easy to make a notation mistake and if you see above a notation mistake means that the reader often has to duck credit for that sorry about that Oh Josh alright so number nine is we’ve title this one know the score and this is a lot about the structure of the exam and how the scores are put together to reach an overall total so the it’s two parts multiplechoice is worth 50 points possible so half of the total exam possible you get one point two five points for each correct answer basically there’s forty questions it gets scaled to 50 by multiplying by 1.25 and you want to answer all the questions unlike some exams like the current SAT there’s no penalty for guessing I in some exams you might lose a quarter point or something like that for every wrong answer but that’s not the case with ap statistics you want to answer every single question there’s no penalty for guessing at all the free response it’s also worth 50 points half the grade and it’s divided into two parts well actually cracking out for a second is 0 to 4 on each question so and there are integer scores so you get a 0 1 2 3 or 4 the questions 1 through 5 are intended to be a little bit shorter and they’re each multiplied by 1 point 8 7 5 to get a total of 37 point 5 points for one through five together question six is a different animal it’s called the investigative task and we’ll talk more about that later it’s worth more than any question on the exam by itself it’s worth oneeighth of the entire test score so you want to make sure and give some good attention to question six then what students always ask me is how well do I need to do to get a certain grade on the exam how many points do I need to get a 5 or how many points do I need to get a 3 so we have an example from 2012 if you’ve got 70 out of 100 that resulted in a 557 out of 100 resulted in a 444 out of 100 gave you a 3 and 33 out of 100 gave you a 2 now those distributions will change from year to year because exams are harder some exams are harder some exams are easier I just gave my students a practice exam from 2007 where the cutoff for a 5 was a 63 so that was comparatively a harder exam the main message for both teachers and students what you want to convey is that the AP exam is harder than a typical classroom test it covers obviously the entire year and there’s also a variety of questions some are easy some are medium and some are deliberately challenging so you don’t want to stress out over a question or two even if it’s a free response question if a student misses Part B or knows that they can’t do Part C on a question it’s definitely not the end of the world there’s a lot of room for missing questions here and there and still getting a really high score on the AP exam so don’t stress out know that in a typical year 70 or 75 is going to get you a 5 you know 4045 points out of 100 is going to get you a 3 knowing that hopefully will release an anxiety for students while they’re taking the test all right Darren up to you for number eight number eight has to do with pacing yourself I’m oh boy Sexton you’ll have 40 questions and 90 minutes so that leads to minutes per question and an additional 10 minutes to check your work go back and look at questions that you may have skipped initially so that you’ll have I think ample time on this section of the test many of my students are able to finish a little bit early even as they go back and check work and reread questions that they weren’t sure about in the first place most most important advice is not spend too long on any one question although it’s generally true that the questions get slightly harder as you move forward towards number 40 it’s not strictly true so you may find question 38 challenging but then question 39 is something that is really comfortable so they’re all worth the same amount it’s not worth spending five minutes struggling on one question that might cost you two other questions that you’re really comfortable with as I mentioned the questions generally get harder towards the end so it might not be too surprising to find a couple of questions in the 30 to 40 range that are they’re challenging that you might want to take a look at and decide whether to skip on the first path the multiplechoice section usually the the pacing is reasonably good if you don’t get bogged down on a question the free response section is a little bit different story again Josh mentioned that that there really are two pieces to the free response section questions 1 through 5 and then the investigative task all told you’ve got 90 minutes to complete this but it’s really important question 6 count for one eighth of the total exam score not to run out of time there so a little bit of additional information on that is s2 gated tasks it’s important that students know that question 6 is going to ask them to do something they’ve never done before the questions are really cleverly written so that they may start out with something that students have seen and then build on that and gradually move outside the box what I find really interesting is some of my students who might not be able to answer one of questions one through five successfully can often make really good progress on question six because they’re just creative thinkers I know there are times when some of my students have outscored me on question six because I kind of know the basic techniques really well but then getting comfort by trying to think in a new way so I think these are really fun problems to to try they are going to require some creative thinking to be able to get a four but it’s very doable for for students to be able to earn at least a two on this question if they just attack it in the way that the questions organized my advice to my students is always to start with questions they feel confident about so I’ll have them look at questions one through five and at this point in the year they know their strengths and weaknesses pretty well so they will gravitate towards usually question one because it’s meant to be fairly accessible to everyone on the exam to get everyone off to a good start and then two or so of the other four questions maybe they’re really comfortable with questions about normal distribution and there’s maybe they’ll see a question about that my students tend to actually really like hypothesis testing and confidence interval because we’ve done them for quite a while now and so they’ll tend to gravitate toward those some of my students really enjoy the questions about surveys and experiments and when they see that question they’ll they’ll go attack that one but none of my students will save question six until the end that’s something we’ve worked really deliberately on it is possible that if you get bogged down in a question on the free response section you will run out of time so if you’re going to run out of time you don’t want to run out of time before the one that counts one eight sub C of the free response course so free advice start with question one but don’t feel obliged to work in a linear order after that it’s usually pretty straightforward hey Josh over to seven all right I wanted to add one thing to the pacing issue and that is I teacher in a workshop who told me a story about how he had a student that was quietly waiting for the Proctor to tell him to move on to question six after he finished questions one through five because there’s a new set of directions for question six even though it’s the same instructions it’s sort of designated separately and then the Proctor said time is up and then you know he didn’t have time to do question six at all so let your students know that in the layout of the exam there’s sort of a new heading a new set of directions for question six but they’re allowed to go in any order and that’s what we don’t save question six till the end all right so now on to number seven which is be smart with technology the first tip is to not type data in just because it’s there I’ve been talking with my students about this a lot recently that a lot of times they’ll provide the data but then they’ll also give summary statistics like the means and standard deviations or the equation of a least squares regression line and in many cases they don’t actually need to use the raw data they can use the other information provided a follow up to that is that if they do provide both the raw data and the summary statistics you can use those summary statistics as a doublecheck to make sure that you’ve typed in the raw data correctly that’s a nice way to use that information if you do need to type in the data the next big issue and this is one that comes up a lot on the AP teachers community is how to address the use of the calculator on the exam and so there’s been there’s a range of opinions and there’s a range of strategies that teachers use both in their class and on the AP exam so for now what I’m speaking to is is how things work on the AP exam you may or may not make different choices you know throughout the year in your classroom but the bottom line for calculator notation or what we call calculator speak is calculator speak alone will not get you full credit there’s an example there with a binomial distribution typing in binompdf 12 comma point 2 comma we will not earn full credit and what I tell my students is they need to imagine that the person grading their exam is a you know sixty year old college professor who uses a computer and is never once picked up a graphing calculator and although the grater will probably be able to figure out what each of those numbers means it’s really the job of the student or the responsibility of the student to clearly communicate the method so if they can imagine that they’re talking to somebody that’s never used a graphing calculator before they’ll realize that that first line there isn’t sufficient for good communication so instead we’d recommend either using the binomial formula which you see 12 choose 3 and so on or using the calculator command but annotating your entries like instead of just putting 12 put N equals 12 and P equals point 2 and K equals 3 those are standard statistical symbols and notation and then whether or not you’ve used graphing calculator before you know exactly the parameters of that distribution the same thing would be true with number 2 the example of number 2 with normal CDF my students love using normalcdf especially when they’re going between two boundaries like this example it saves a lot of time but if they just put normalcdf 90 comma 105 comma 100 comma 5 that will not result in full credit even if they get the answer correct because again it’s not good communication so instead students can find the zscore draw a shade and label a normal curve and then find the area using the table or using normalcdf or they can use the normal CDF command as long as the entries are annotated so instead of just putting 90 comma 105 they put lower bound equals 90 upper bound equals 105 mean equals 100 and standard deviation equals 5 now I want to piggyback for just a second on something that Darren mentioned in passing a few slides ago and that is the difficulty of using symbols correctly so we know that there’s lots of different standard deviations that show up in our course it could be the standard deviation of the data of a sample could be the standard deviation of a population it could be the standard deviation of the sampling distribution of xbar and all of those have different symbols so I have my students instead of trying to pick the right symbol just write out the word mean and write out you know SD or STD de vie for standard deviation and so they’re not putting themselves out there and possibly using an incorrect symbol so the the summary of this is it’s perfectly okay to use technology as long as it’s clearly communicated so that somebody who is not familiar with the graphing calculator will be able to understand what the student is doing all right on to number six all right tip number six and this refers specifically to inference questions on the free response section so whether you’re calculating a confidence interval or performing a significant step we strongly encourage that you follow the four step inference process when running up solution we’ve made a copy of the four step inference plan for both confidence intervals and tests and this is from our long experience working with the rubrics for scoring these problems in any significance test rubric there are going to be four elements that the grater is going to be looking for we’ve chosen to call them state plans do and conclude but in the state park the grater is going to want to see the hypotheses carefully stated any of the parameters that are used there need to be correctly labeled so mu for population mean P for population proportion and in some cases the question will will require a definition of the parameter so the Muir the P has to be carefully explained then in the planned step the expectation is that the inference procedure will be named so one sample ttest for example it’s also possible to identify the inference method giving the formula for that method as part of the calculations but it’s someplace in the solution the inference method has to be identified and also as part of the plan steps the conditions for using that inference procedure need to be clearly identified and checked using the information provided in the problem so for instance if you’re wanting to do a one sample ttest and it’s important to check that the data came from the random sample or a randomized experiment of some kind and also to check the normal large sample condition so you need to either have normally distributed population or large sample size in the do step students can do one of two things they can show the numbers substituted into the formula to get the test statistic or use the calculator stat test menu to get the test statistic and the pvalue can also be obtained through the stat test menu so it’s absolutely legitimate to write down the test statistic and pvalue from the calculator and any degrees of freedom if those are appropriate for that problem the advantage to showing the work inside the the formula but the numbers in the formula is that some partial credit could be available then if you only use stat test then it’s either an allornothing proposition if you put information into your calculator and then write down the test statistic and pvalue it’s either right or wrong so to be honest I encourage my students to use stat tests I think they’re more effective that way they’re more likely to get it correct on a consistent basis down to occasional typos then the conclude step we’re looking for a clear decision about the null hypothesis to either reject or fail to reject the null based on these calculations that were done that clearly links the pvalues to a significance level so hopefully the significant soul has been stated at the beginning and now we’re just comparing that pvalue the significance level in making the decision and then some contextual conclusions that talks about the strength of evidence for the alternative hypothesis so it’s really two distinct sentences if my students are writing it the first one has to do with sort of reject or fail to reject the null hypothesis based on how their pvalue compares to their alpha level and the second sentence is about whether they do or don’t have convincing evidence for the alternative hypothesis written in context the confidence interval side is a little bit easier because the there are no hypotheses so we’re just thinking about what we’re going to estimate and at what confidence level so a clear statement of the parameter really helps students get a good contextual conclusion at the end of the at the end of the problem the planned step is the same as I mentioned before and the calculations are the same as I mentioned before you can use stat tests or stat intervals depending on the calculator do the do step but the risk is it’s an allornothing proposition again I want to recommend that writing out the symbolic formula with for example xbar plus or minus e star times s over root n is really risky my students tend to make notation errors and then the greater has to do as I said earlier and and do a mandatory deductive another suggestion related to this fourstep process becomes the grading rubrics are set up this way it it makes it easier on the grader if the student labels what they’re doing in each of these in each of these steps so something like hypotheses conditions calculation and interpretation or state plan do conclude is much appreciated by the greater it makes it easier for them to match the solution to the grading rubric and I think quite often students who organize their work in this way and to perform fairly well it’s the safe bet that at least one free response question will require the entire four step process and it’s possible that there might be a second one on some exam so I don’t have a crystal ball I don’t know what will happen this year but I’m at least 99% confident that one problem will require a whole four step inference problem that the wonderful little inference review as Larry green websites Lake Tahoe Community College so I’m just going to try to launch that link and then in just a second we’re going to be taking some questions so this is Larry Greene’s website at Lake Tahoe Community College it’s a wonderful opportunity to practice identifying which is the correct imprint method from among all the ones we’ve studied this year so from this site if you click on select all and then deselect oneway analysis of variance and deselect predictions for a single value of y for a fixed X those are two that we we don’t really cover in detail or at all in the AP statistics course and then once you’ve chosen your options you just click Submit and some kind of research question will come at the top box so this one is interesting do college students listen to the same radio stations as the general public two thousand college students were asked what radio station they listen to their choices were compared to the known overall ratings so this is a little bit vague and deliberately so have to think about what kind of procedure is being asked for what I like is it first of all forces the decision between a confidence interval and a hypothesis step so the question is are we trying to estimate something where are we trying to test a claim about something and the wording in the first sentence here seems to suggest testing a claim about whether college students listen to the same radio stations with the general public that doesn’t sound like an estimation question I’m singing test and then we have to identify what type of test is the test about a mean assess develop proportions test about a difference between two parameters or possibly a chisquared test that has to do with distribution of categorical variables or relationship between category variable so my reading is this so sounds like we’re talking about the distribution of a categorical variable which is radio station preference or primary radio station you listen to and I’m looking at the distribution of listening preferences among college students so I’m going to try and get something here just so you can see the feedback oh good for me always risky when you do one live and cold that you might miss it but you do get immediate feedback and if you get it wrong you actually get a hint to get you back on the right track so suppose I take the wrong kind of chisquare test you see the feedback perfectly safe and then we can get a little hint here about testing for a distribution not independent so good job we got it right amid them at this point I think we’re going to offer up the questions at all great we do have a lot of questions that came in while you guys were talking so I will start with those if anyone has more questions feel free to send me a message using the chat not the Q&A so the first is from Jan a and it is can you explain the difference in blocking and stratified sampling what are the correct definition okay this is this is Josh um basically stratified sampling happens when you are selecting a random sample from a population when your goal is to estimate some characteristic of a population blocking happens when you’re assigning treatments in an experiment and that’s the key difference is stratified it’s a technique that you can use when you’re doing a sample and blocking is a technique that you can use when you’re assigning treatments and in experiments they have a lot of the same benefits and they sound very similar because you start by forming groups that have some characteristic that you think is going to be related to what you’re measuring but again stratified happens when you’re sampling and blocking happens when you’re doing an experiment okay thank you the next one is if you show the symbolic formula while answering a question you have to explicitly name the formula so okay agreed the next question is on the free response on average how many concepts are on each question since the exam is covering the course as a whole that’s a good question I’m not sure that there’s a an easy answer for it I know that when I was on the test Development Committee we are very conscious of trying to match the percentages that are in the course description things that say like collecting data should be 10 to 15% so we made sure that you know no more than one essentially one full item was about collecting data inference on the other hand was 30 to 40 percent so we’d keep careful track even if questions were split you know maybe one part on question one and two parts on question two we kind of add those up to make sure that they fit within those guidelines you know but inference there’s a lot of inference right that’s five chapters in the book so it could be that there might be a you know one sample T interval for a mean and then a chisquare test and we never do anything with Z test for proportions it’s just hard to know on the multiple choice though of course with 40 questions they are able to get a lot better coverage of the entire content so I know that wasn’t an exact answer to your question but hopefully it helps a little bit thank you the next question is from Jeff see I always tell my students to show the work for the test if it’s sophistic when conducting a hypothesis test yet every fr rubric indicates the student only needs to name the test or show the formula and give the test statistics and pvalue is there any advantage to showing the work for the test statistic will a student lose points for a formula shown with wrong values but the right test statistic and pvalue sounded like a multipart question very highspirited so there there is a potential advantage to showing numbers substituted into the test statistic formula and that is if the number substituted into the formula make for a correct formula for the test statistic that’s going to probably be at least partial credit if there’s then a computation error on the test statistic then we’re still at partial credit if the student does not show any work at all and just goes to stat test and provides the wrong test statistic and wrong pvalues there’s really no credit there there’s no way for the grater to have any idea probably what the student did so I think the other part of the question was if a student shows a formula with numbers substituted in and the formulas not right well that’s going to have to count off so if the student gives the correct test statistic and pvalue from the calculator we’re sitting with full credit for the do step but if the student then provides a formulaic attempt to support that and the numbers are plugged in and it’s not equivalent then then it sounds like we can’t have full credit Josh would you agree yeah I absolutely agree and what I do with my students during the year is different than the advice I’d give right now I found that very few of my students make typos but lots more of my students have trouble executing the formulas correctly and getting everything done that way so my strong recommendation to my students at this time of year is to use the stat test menu for the the test statistic and the pvalue or the end points of a confidence interval if it’s a confidence interval question understanding that there’s a risk of a typo leading to no credit that’s a much smaller risk for my students than the risk of trying to do it by hand and then messing up somehow or coming up with an answer that disagrees with the with the calculator answer Nicole I’m sort of keeping an eye on the the clock I wonder if we should maybe do do a few more slides and then we can do one more batch of questions at the app sure um we do have three four five six you’ve got seven questions on tap so okay then we should definitely move on I think and if people want to sign off before the you know when at the end of the slide that’s fine it or they can stick around and listen to the questions also alright so number five actually we’ve kind of talked about half of them it’s a naked answer equals no credit so I’m not sure where that that phrase came from exactly but what we’re talking about here is an answer with no supporting work and so we wanted to quote you these are the directions that students are supposed to read at the beginning of the free response section says show all your work indicate clearly the methods you use because you’ll be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations and this is really true we hold students to this the problem are the most common time when this comes up as an issue is on probability questions where students can maybe do something either in their head or on their calculator and they’ll get an answer they’ll write it down without any supporting work and at best that’s given partial credit okay there is a slight exception to the rule and that’s what we’ve just been talking about this question about using your stat test menu for inference questions for the do step the pvalue and test statistic or the endpoints of the confidence interval I put exception in quotes because it’s not really a violation of this because students in the previous step the plan step as we call it will have identified the procedure say a two sample ttest or a one sample Z interval for a proportion or something like that so that identification of the process is the work is the justification for the method and then you’re just reporting the values from your calculator at that point now we’ve talked about the potential drawbacks and I just wanted to add one more thing on that is when I’m teaching this during the year when we’re going one chapter at a time I prefer to have kids you know work with the formulas so they get some practice so they know how they’re developed and also so they’re able to handle multiple choice questions that may focus on aspects of the formula for the test statistic or the confidence interval all right let’s move on to number four this is a common theme that my students that I talked about leading into the exam now many of the questions on the AP exam students are forced to side between which of three distributions are being talked about at any moment one is the distribution of sample data that could be quantitative data we might be looking at a dot plot of some sample data or it could be categorical data we’re looking at a bar chart of some kind or the problem to be talking about the population distribution of some variable and again that variable could be categorical so the population distribution could consist of the percent in each category or it could be a quantitative variable so the population distribution we just imagined might be might be a normal distribution or we could be talking about the sampling distribution of a statistic like xbar or PDF so that is the value of the statistics in all possible samples of the same size taken from the population and often the sampling distribution of the statistic follows a nice normal distribution pattern approximately if certain conditions are met so distinguishing the convened these three distributions is difficult you have to read really carefully to see what the question is asking so here’s one example from a recent exam big Tom Fisheries recently stocked a new lake in a city park with 2,000 fish at various sizes the distribution of the links of these fish is approximately normal timeout which distributions are we talking about well it’s announced to me like that all the fish I think we’re talking about the population distribution of length like being a quantitative variable and we’re told that it has approximately a normal distribution now let’s look at Part A of the question Big Town fisheries claims that the mean length of the fish is 8 inches so that’s the claim about the population needs you if the claim is true which of the following would be more likely a random sample of 15 fish having a mean length that is greater than 10 inches a random sample of 50 fish having a mean length that is greater than 10 inches justify your answer so this one is the tricky one we’re hearing something about a random sample so we might be thinking about the distribution of the sampled data for those 15 fish which could be a dot plot for example and the same for the random sample of 50 fish but to answer the question we need to know how the sample means would vary in random sample of size 15 and how the sample mean would vary in random samples of size 50 so this is actually a question about the distribution of sample mean and you can see from the scoring guide that the part a is scored essentially correct if the student says that the sample of 15 fish is more likely to have a mean length that’s greater than 10 because it’s much there’s going to be much more variability in sample means for samples of size 15 and for samples of size 50 or put another way you’re more likely to get closer to the truth about the mean length of the fish if you take a larger random sample then if you take a smaller one so you can see the justification in this problem has to be based on the variability in the sampling distribution of xbar so all the elements are shown really nicely in this question and I would say that on each year’s exam you’re going to find at least one question like that okay Josh I think we’re on to number three all right number three is don’t write too much this is an interesting contrast to number five which was make sure to justify your answer and show work and communicate there’s a fine line to be drawn between saying enough and not saying too much so the first tip is less is more and that is the best answers actually tend to be quite short and to the point you don’t need to go on and on I think there’s a belief that a lot of students have from their other classes maybe an English class or a history class that they need to write as much as possible and just dump their brains out onto the paper that’s definitely not true here and as we’ve talked about if you go on and say things that are incorrect and contradictory you’ll lose points okay so the second point second tip says to answer the question in context and then shut up be quiet so many kids lose credit because they just keep going on and we say in the trainings now had they stopped after the first sentence they would have scored E but if we continue reading we’ll find out and then the scores go down the third point is that space provided on the exam is typically more than enough there is careful thought to how the questions are laid out on the page and where parts start and where parts end students can use that as a rough guide but they’re almost never intended to fill the entire space the fourth one is to avoid parallel solutions and we’ve kind of referred to this already but the idea is that students will be graded based on the weakest of their responses so if they attempt to answer a question two different ways for example using their calculator and using a formula students will be graded on the weakest response that way we discourage kids from just trying thousands of different methods hoping that one of them is correct the next point I don’t interpret the pvalue or the confidence level unless asked to we find that you know it perhaps is good teaching during the year teachers will reinforce you know asking students to interpret the pvalue or interpret the confidence level just as sort of regular practice but that’s not part of the four step process that’s required for typical inference questions by interpreting the pvalue I mean something like assuming the null hypothesis is true there’s a suchandsuch probability of getting results like hours or more extreme by chance alone or the confidence level would be treated lots and lots of random samples of this size and computed lots and lots of intervals from those samples about 95% of the intervals would capture the true parameter those are good interpretations that students should be ready to do if they’re asked to but they shouldn’t volunteer those as part of a regular inference question because students honestly mess them up quite easily and that will lower their score the last one is to not argue with the test writers believe what they tell you so if they say the conditions are met say thank you and your head and just move on or if they say that everybody is going to respond to the survey even though that may not be true and realize if they tell you everybody will respond in the survey then just believe it they’re trying to make make it easier for the students so don’t argue with the question writers all right that’s number three king of the questions this is one of my simplest pieces of advice that I use with my students all year long often when I give papers back they’ll have a little acronym rtq or a TQ rtq simply means read the question sometimes if you don’t read very carefully you go off in a different direction than what was intended and my other favorite is a TQ answer the question it’s amazing how many times we look at a response on the free response section and the student didn’t actually answer the question that was asked they may have answered a different question that was pretty interesting but we can only give credit to answers that head toward the one that we were expecting so if a question asks you to do each of the following make sure you for example if a question asks you to describe a distribution of a quantitative variable there expecting discussion of shape Center and spread that’s that’s a prompt that students should know by the end of the course if the question asks that students compare distribution then it needs to be comparative about the center which one has a higher or lower center which which distribution has more or less variability than the other question asks you to describe similarities and differences then that’s what what’s expected all of these have appeared on different exams and in each case I’ve seen students follow one of the other sets of directions besides the one that was given if a question asks you to explain or justify then obviously that’s something that you’re going to need to do to get full credit and this is the trickiest one of a question is a compound question that asks you to do more than one thing for example find the mean and the standard deviation of a random variable or calculate and interpret a confidence interval the student has to do both things in order to get up to get full credit so it’s really important that you read the question carefully and then be sure that you’ve answered the question that was asked if it’s a yes/no question that you need a yes or a No and you need justification okay Josh number one number one be prepared so one thing you can do to be prepared review the formula sheet and the tables that come on the AP exam I find my students do use the tables lots of times they don’t use the formula sheet but it’s good to know what’s on the formula sheet so that if there is an issue you can go look at it and maybe looking at the formula sheet will help prompt you and trigger something in your brain so know what’s on the formula sheet know what the formulas refer to and know how to use the tables that are provided and just so you know the formulas and the tables are provided on both sections of the exam the free response and the multiplechoice the next tip is to do lots of practice AP exam questions including as you’ll see a full length exam if possible it’s nice for students to have the experience of sitting for a three our statistics test to have to stretch their brain for that length of time and covering the entire course and if you have an opportunity to do that I’d be nice to focus on more recent exams you can find in your AP audit account recent exams that have been given internationally these exams of course are secure but you can use those with your students in class you can also assign released free response questions from AP central to your students and as a general rule I’d recommend that you focus on more recent exams there are course good questions on older exams but the more recent exams will be better indications of the kinds of questions that are being asked and the scoring guidelines will be more reflective of how questions are being scored nowadays also the third thing to identify weak spots and focus on them so there’s a couple ways to do this one of course is the fulllength practice exam that covers the entire content you can tell by the kinds of questions that your students are asking after that or if you grade it yourself you can see where the weak spots are and focus on them also for teachers after the AP exam and after the scores are released in July maybe sometime in August or September you’ll be able to get an instructional planning report that talks about how your students did in each of the four major content areas is descriptive statistics collecting data probability and inference I know my students typically our week in probability so we’ll do lots of extra practice questions about probability leading up to the AP exam and then the last thing for preparing students is to give them a set of flashcards that we have available on the teachers resource materials for both TPS 4e and 5e for TPS for users they’re in the binder at the very back for 5 EU tzer’s there’s no print binder anymore but if you have the teachers resource flash drive if you look in a chapter 12 folder for the teachers resource materials you’ll see a PDF of the flashcards there there’s a set of 80 flashcards that review all the key ideas from the course every year my students report back to me that they were very glad that they went over the flashcards as they were getting ready for the AP exam because several of the concepts that they’ve been reviewing showed up on the exam and they felt much better prepared because of that all right so that’s number one so we’ll go ahead and count down the top ten tips again you can see them flashing up there on their screen and the very last note is for questions so Nicole you can go ahead and read out some of the questions that have come in great so we do have a lot of questions that have come in the first is from Jan a what about using panicked for confidence intervals and phantoms or hypothesis testing as a guide and for those of you that don’t know panic is parameter assumption same test interval conclusion and phantoms is parameter hypothesis assumptions name test test statistics obtain pvalue make decision date conclusion this is Josh I think that’s a fine thing to do if that helps your students I prefer our fourstep state plan do conclude I find that students when we look at rubrics or scoring guidelines they find it very reassuring that the the four steps I’ve been teaching them match up with the four steps that are being assessed on the rubric but that being said numbers of students use those panic and fans acronyms as a way to organize their answers and to remember the steps so I think you know if it works for the students and they can answer the question successfully that’s fine I have to be careful on this one my colleague who teaches says ap statistics next door to me uses those two acronyms with her students so although the state plan do and concluded my favorite of the other acronym seems to work pretty well for her students next question next question is again from Qian a sometimes in the book and she’s using TP s3e the assumptions aren’t really met yet so I tell students to do two calculations anyway but what should they say in the free response section to note that assumptions may not be met we have good news for you there if the question on the free response section asks the student to calculate a confidence interval or perform a hypothesis test the good news is that the conditions are going to be met so students don’t need to worry about that if they’re they’re actually asked to do calculations they’ll be provided with these or reassurance that the conditions are met or they’ll be given the appropriate information to verify that they really are met it is possible that there’ll be a question somewhere on the exam that focuses in on a situation where we’re just checking conditions and in that case the conditions may or may not be satisfied but in a free response question where students are asked to do the fourstep process the conditions will be met I agree next question the next question is from Steve see my students want to know if anything has changed for this year’s exam by way of grading or content not that I’m aware of they certainly haven’t made any announcements on the AP teachers community or on AP central so everything is the same as last year in the last several years I agree the next question is from John T for listing the inference method in the fourstep process is it enough to list what function on the stat test menu of the calculator was used I am thinking no but I feel like my students have gotten into that habit yes it is enough that’s sufficient to call it to Sam ttest or to prop Z test is sufficient for identifying the procedure yeah I would agree the only followup I would add is that’s on the weak side of communication it would get credit but if a student was you know at a two and a half or a one and a half and a grater had to make a decision about whether to take that two and a half up to a three or take that two and a half and move it down to a two very minimal communication usually is not a point in the favor of the student so it is sufficient but if you can encourage them to write it out you know maybe with a more complete name that would be a that would be helpful okay next question next question is from Toni s our students required to use a pencil or can they use a pen on the AP exam is one preferred over the other especially on the free response different AP exams tend to require different types of writing instruments yeah good question um certainly on the multiple choice kids do use pencil and on the free response I’m not sure if there’s an official requirement but I’d say 99% of kids are using pencil on the papers that we see so I’d recommend pencil the next question is from a meat beef can you give a good way to explain the difference between lurking variables and confounding and what is the best way to explain what our upper carrot to represent I’ll take the first one okay I’ll do the second one my best advice is not to use the term lurking variable at all on the exam it’s not commonly agreedupon term out in the statistical community and in fact those of you who are using the fifth edition of our book bowl will notice the disappearance of that term it’s been a term that’s been around for a while and certainly if it means more than one thing depending on who you ask so I sort of prefer to call those things other variables rather than coming up with a fancy name to them so other variables besides say the explanatory variable or the response variable this is a much safer term that would be accepted by anyone the term confounding is definitely on the AP statistics topic outline and it’s one that if you’re going to use you need to understand that for there to be confounding the relationship between the explanatory variable and the response variable has to be blurred by this other variable I’m not going to use that l word but the other variable has to be associated with the explanatory variable and also it has to have some clear relationship to the response variable so confounding is a complicated situation where another variable is linked to the value of the explanatory variable and also clearly has a relationship with the response variable so this is Josh now these are two of the issues the idea of confounding and the interpretation of rsquared that my students find the hardest and on the you know it’s a grading we find that students typically do the weakest so very valid questions so R squared is usually arises when we’re talking about regression and basically rsquared is trying to answer the question how much better will my predictions be if I’m allowed to use the X variable along with the least squares regression line compared to not being able to use the X variable so we have an example now in the in the fifth edition where we try to predict the price of a used truck based on the number of miles that it’s been driven and so I tell my students well suppose you just see a truck driving down the road and you see a for sale sign in the window but you have no idea how many miles it’s been driven you can still predict how much it would cost you just use the average cost of all the used trucks that you have but that prediction would not be very good you know that you can make a better prediction if you knew how many miles it has been driven so you could make a scatterplot in with number of miles on the xaxis and price on the yaxis and fit of least squares regression line and make better predictions so rsquared essentially measures how much smaller the sum of the squared residuals are when you get to use the least squares regression line compared to just using the average value of y and since it’s a percentage so if rsquared is say 38% that means that some of the squared residuals are 38 percent smaller when you’re using the least squares line compared to just guessing the average value of y so that’s the long explanation that I try to give my students to help them make sense of it the standard interpretation that you’ll hear is really just an abbreviated version of that and they’ll say something like 38 percent of the variability and price is accounted for by the least squares line using x equals miles and that’s basically a statistician shorthand that often doesn’t carry much meaning for students so I like to make sure they understand the longer explanation or the longer story but I make sure to expose them to the sort of abbreviated interpretation also because I’ve seen that used in both free response questions and multiple choice questions all right so this is Darren again I just want to acknowledge that we’ve reached the one hour mark on our webinar and I know Josh and I are very happy to stay and continue answering some questions but we also understand it if people have other other plans and we’re still recording the webinar so don’t worry that you’ll miss something you can always play it tomorrow what once the call up was the link but I just I wanted to take a moment to thank everybody for joining us and hope that you’ve gotten a lot out of it and as I say we’ll be glad to stay and take more questions absolutely we have about eight questions left on tap and if anyone has any more you can send them to me using the chat function and I want to thank you guys again for joining us tonight so the next question is from Mary B and this is from her students what concepts are most frequent on the exam what is the balance between conceptual questions versus Gilbey’s questions on the multiple choice could you repeat the last part of the question Nicole sure what is the balance between conceptual questions versus skill based questions on the multiplechoice okay on the multiplechoice I think that there’s a real effort to ask conceptual questions there’s not I mean there’s no question that for instance would say you know here is eight numbers find the median which I would call a skillbased question that we might ask you know at the very beginning of the course most of them are conceptual and my students will tell me that they don’t use their calculator very often especially on the multiplechoice section because again most of the questions are tend to be conceptual on the free response you’ve probably seen more free response questions there’s a mixture of conceptual and sort of calculation or skill questions but again I would say that there’s a different favoritism towards conceptual questions the next question actually came from a few people so I’m just going to paraphrase um how much folk penmanship or sloppy handwriting affect your grade if you have bad penmanship will readers for you again a little bit worse this is Darrin I’ll take that one the answer is we will try our best we’re at the grading we each each reader has a partner and so if the initial reader can’t read the handwriting for whatever reason they will contact their partner and ask for them to try to read it if if they’re both having troubles and we have someone else in the grading room called the table leader that they can take it to and the table leader also has a partner so to be truthful if the writing is really difficult to read we’ll give it up to four accounts just to make sure that we’re giving it a fair assessment and at that point if none of the four people can really make out what’s going on and at that point we really can’t really can’t spend any more time trying to trying to read it so four or four attempts is as much as we are able to do but a good effort stride is made to try to read each students answer so not I guess the direct answer the question is not beautiful handwriting shouldn’t really impact the score but illegible handwriting so illegible that four people aren’t able to read it could definitely impact this court all add also that spelling doesn’t count for the most part so I know I have a student who has some issues with spelling and I’ve assured her that as long as we’re pretty clear what word she’s trying to spell that you know spelling incorrectly is not a not a big deal don’t let the English readers hear you say that so the next question we’ve about six left the next question is from Melissa B how exactly do you practice rule number four which distribution effectively with your students so that they feel prepared and confident walking into the exam this is Josh I would do exactly what Darrin did is he was highlighting the slide which is as you’re reading a question or talking about a scenario every time that there’s mention of a distribution or some measure of center or variability that you stop and you say now which one is it referring to another way that you could do this is to use a couple different applets that we highlight in Chapter seven which is a sampling distribution chapter there’s one that’s a we call it the rice online sampling distribution applet it’s not produced by us but it’s really good because it on the top it shows a population on the next level it shows a sample and then right below that it shows the sampling distribution of a statistic typically the mean and really showing all three of those distributions on the same screen and then being able to talk about it I think really helps students begin to clarify which one is which Darrin’s going to go look for it right now yeah go ahead with another question and I’ll find it here in a second okay the next question is from Julie C inference on the exam did I hear you correctly when you said we never do is the test for proportions no we can do Z tests and Z intervals for proportions I think the possible a correct statement might be that we don’t do a Z test for a mean or Z interval for a mean that would only be the case if you knew the population standard deviation Sigma which is almost never never the case so definitely okay to do a Z test for a proportion or Z test for an interval or a difference z part of a Z test for a proportion or is the interval for proportion or difference in proportions looks like Darren is ready to demonstrate the applet yeah this is the online stat book applet for sampling distribution you can see this is the population distribution at the top is approximately normal or normallooking and if I take a sample it will display the distribution of sample data here and then it will drop after it takes a sample of size 20 it will drop the mean down onto this next set of axes here so if we do a bunch of those we can get a picture of the distribution of sample mean but I think the best part is seeing this picture with the population distribution the distribution of sample data and then the sampling distribution being built up of xbar and you can see that each of those distributions has different spreads and different shapes or well in this case you know two of them have normal distribution shapes so it’s always very important that you don’t ever say there’ll be more variability you need to say there’ll be more variability in the distribution of blank depending on which distribution you’re talking about so it’s getting students to be precise with their language that’s the real key here all right other questions um the next one is from Jasmine G what would a regular inference question that doesn’t ask to interpret the pvalue or confidence level look like so typically the confidence interval questions will start with a statement like construct and interpret a 95% confidence interval for the mean blah blah blah or the proportion of you know people who blah blah blah something like that but it’s the construct and interpret that will trigger kids to do the four step process and when it says interpret we’re talking about interpreting the confidence interval itself saying something like I’m 95% confident that the interval from two point eight to three point nine you know captures the mean GPA for students at our high school or something like that and for tests the wording typically will say something like do these data provide convincing evidence of or something to that extent in which case that’s a trigger to do the four step process with the significance test if it wants students to interpret the pvalue it’ll say interpret the pvalue if it wants them to ensure for the confidence level it will say interpret the confidence level or maybe something like what does it mean to be 95% confident in this context the next question is from Corrine B should students be proficient in using the tables or is knowing the calculator okay this is Darrin my students tend to use the calculator more frequently at this point I have a few students who who prefer the table and they’re they’re certainly welcome to use the table throughout the exam there might be an occasional question in the multiple choice for example we’ve actually run into one very occasionally in a part of a free response where students felt like looking up something on the table was helpful but for the most part I would say the majority of my students are comfortable just using their calculators what about yours – for the most part yes certainly with normal distribution questions where my students tend to use the table more often than the calculator is when they’re trying to get a T critical value for a confidence interval they’ll often feel better with the table because they could just look for the the bottom of the table that gives them like 90% 95% and so on with the degrees of freedom but for the most part on inference stuff now they’re using the the test menu which provides that information for them so that might be more of a multiple choice type of issue where they might use the T table for a critical value all right we’ve said more questions this one should be a quick one our mechanical pencils allowed on the exam yep yeah I have students ask me that every year I’m not sure the concern but my students use them all the time and they’ve never had any trouble the next question is from Becky G as a followup to the penmanship question how closely is syntax and correct use of English graded I have a large number number of English language learners for whom writing explanations is difficult so this is Darren I at a boarding school so I have a number of students who are international students and that is that this is not the AP English exam where we’re concerned about student statistical knowledge and their ability to communicate their statistical understanding so unless the structure of the writing gets in the way of that objective the readers are really going to be forgiving with awkward sentence structure or faulty usage I can’t think of too many cases where I found that students use of the English language has gotten in the way very occasionally though so I hope that was a clear enough answer yes and I agree the next question is what was your recommendation regarding pooling I have gone with this book answer but then I’ve seen old free response question affected pooling so pooling generally just means combining data to come up with a better estimate for something and depending on the situation pooling is appropriate in some cases and not as appropriate in other cases so for example when we’re doing a twosample ztest for a difference in proportions the null hypothesis typically says that those two proportions are equal to each other and the calculations in a significance test are always based on the assumption that the null hypothesis is true so we’re left with a situation where we have to assume that those proportions are the same but we don’t know the value of either of them so that’s a case where we do pool the proportions or pool the data do the total number of successes over the total sample sizes to come up with one estimate for the overall population proportion in the book we call that the pooled or the combined proportion the in that case it’s actually not optional that’s what the right procedure is and for instance the to prop Z test on the calculator automatically does that and doesn’t ask students whether they want to pool or not on the other hand if you’re doing a two sample ttest for a difference in means the null hypothesis is that the meet the two means are equal but there’s no statement about the standard deviations needing to be equal so when your calculator asks you whether you want to pool on the two sample ttest it’s asking the student whether they want to combine the data to come up with a single estimate for the standard deviation that requires that additional assumptions are met and it typically doesn’t add much value or much power I should say to the procedure so that the ap stats answer for anything involving the two sample ttest or two sample T interval when the calculator asks you to pool just say no the next question is from D on M if they’re going to be a book map again this year if so do you know when it will be available so Dion I asked some people at NCTM about this and they said essentially not sure we’ll get back to you but I’m guessing at this point that if we haven’t seen a book map for the free response questions we probably won’t and I’m guessing the reason why is that well first for those who don’t know what the question was about the last two years they’ve released a book map of the free response questions which basically gives kids an idea of what each page is going to look like it’ll have a little box that says question is here and then a blank space where you can you know that’s where your answer would go so kids could feel comfortable about the layout of the exam but what was pretty obvious to most of us last year when we saw question five on the book maps there was a tiny little bit for a question and then a really long space for an answer and so we pretty much all knew that was going to be a an inference question you know requiring the four step process so my guess is that they didn’t really think too far ahead on what clues they could be giving with the book map and it probably stopped that at this point the next question is from Julie C well students get a deduction if they talk about central limit theorem instead of just using language large sample size or doesn’t matter and what cut is the cutoff point for n the as Aaron we know that students when they’re doing inference about a mean and they don’t know that the population distribution is normal it’s great that they’re thinking about the central limit theorem and that if the sample size is large enough they’re okay to go ahead and perform calculation as long as students don’t start freelancing beyond that they’re probably okay if they just refer to the central limit theorem and the fact that it is large enough and by large enough in our text we use the criterion of being and being at least 30 on the AP exam they usually go quite a bit higher than that just to be sure that whatever text students are using the requirements are met so as long as the student says n is 50 which is greater than or equal to 30 so the central limit theorem applies no greater is going to object to that Josh you agree yeah I agree but this is one of those cases where it’s possible that saying too much could hurt you if you use the central limit theorem correctly or refer to it correctly that’s great but lots of kids will just put the central limit theorem down on any old question just trying to sound like they know something and of course that could end up hurting them and the last question that we have is a elude D please comment on the use of bullets in free response questions as compared to all sentences well I’ll go first this is Darrin I like students using bullets it helps keep some of my students really well organized so even within each of the four steps of the state plan doing concludes my students tend to bullet individual parts of those like test statistic or pvalue the only the only problem for me is if if a question requires students by saying write a few sentences that’s really a case where the bulleted list is going to potentially be problematic so for the most part I let students follow their own style and if the bullets help keep them organized I’m a fan and I would agree as a reader that it’s a lot easier to follow the students work and be able to identify the things that the student is doing correctly if it’s well organized that doesn’t necessarily mean bullets but it does mean well organized and often times doing it with bullets does help a student organize their response and so generally that’s a good thing and alright one more question just came through from a firstyear ap statistics teacher there any general lastminute advice that we didn’t cover on today’s webinar not really as far I mean I think we hit the main points I would just try to you know spend as much time as possible going through recent AP exam questions so students feel real comfortable with how they’re written looking at the scoring guidelines to see what kind of expectations they have and then reminding them that getting 50% on the AP exam is a guaranteed three and they don’t need to stress out if they’re not getting perfect scores yeah I would agree and I would also add that there’s still plenty of time to improve your score if you’re a student I have students have been working practice questions and making mistakes and like Josh says getting a little bit more than 50 percent correct but if they can if they can improve just a little bit they’re actually within striking distance of earning for so it’s only a little bit of improvement over just a little bit less than a twoweek period I think that’s a good note to end things on so um if you guys do have any more questions that you think of after you’re watching the recording please feel free to just send me an email and I can forward it along we really appreciate you guys giving up your Wednesday evening to join us for this webinar and like I said you will receive the recording by noon tomorrow so thank you so much for joining and supporting us tonight and good luck to all your students two weeks from today yes tell your students good luck thanks a lot Nicole have a good night everybody tonight tonight bye you
Related posts

C# Tutorial For Beginners – Learn C# Basics in 1 Hour
Hi! Thank you for taking my C# tutorial for beginners. Let me quickly give you an... 
WordPress Tutorial: Build Your Affiliate Marketing Sales Funnel
Hi Kevin Barham now and in this shorttutorial I’m gonna show you how to build an... 
Python OOP Tutorial 1: Classes and Instances
Hey, everybody. How’s going in this streaks of videos? We’ll be learning how to create and...