<p>This thread is intended for you if:
a) you are self-studying AP Stats, or
b) your AP Stats teacher has not shown you how to structure your answer to maximize the credit you obtain.</p>
<p>This thread is not intended for you if you have an experienced AP Stats teacher whose good students usually get 5's, or a Stats teacher who actually grades the AP exams. You are welcome to read it, but probably won't learn anything new.</p>
<p>I will be posting a set of suggestions below, because I have occasionally noticed students on the Caltech forum who were baffled at receiving a 4 on AP Stats, instead of a 5, when they understood the material and had 5's on other AP exams. </p>
<p>This thread is not intended to tell you how to carry out a chi-squared test (although there is still time to figure that out if you do not know). It is mainly intended to tell you how to ensure that you receive all of the points you deserve.</p>
<p>The information in this thread comes from our family's analysis of the AP Stats FRQ grading, posted by College Board, from the time when QMP took the exam--so it will be slightly out of date, but I hope it is still useful. The next post starts the suggestions.</p>
<ol>
<li><p>You need to state the problem in statistical form. Frequently you will be asked to obtain a confidence interval or to test a hypothesis. The problem may deal with
a) a population proportion
b) a population mean
c) the difference between two population proportions
d) the difference betwen two means.</p></li>
<li><p>You should explicitly justify the use of a statistical method (that is, write it down in English)
a) The sample must be a random sample. If this is given in the statement of the problem, you still have to write it down, to guarantee full credit (at least, based on our reading of the grading practices). This might trip up people who understand the material, but don’t think they need to echo something that’s right there on the page.
b) The sample must be less than 10% of the population. You should explicitly note this fact. Ideally, you should state the population size, write down 10% of it, and compare the sample size with that. (Yes, it will be completely obvious. But you want to guarantee full credit.)</p></li>
</ol>
<ol>
<li> Now state your method.
a) For a confidence interval:
i. Select a z-test or a t-test. Justify your selection
z-test: Standard deviation is known, or sample is larger than 30
t-test: Standard deviation is unknown, and sample is smaller than 30
ii. Write the interval as a formula, and define the parameters in the formula
b) For a hypothesis test
i. Write the null hypothesis in the form H(subscript 0): blah, blah
Note that the null hypothesis is based on a priori expectations about the actual population. It is never based on the sample data.
ii. Write the alternative hypothesis.
It will have one of three forms: The actual population parameter is not equal to the value assumed in the null hypothesis, the actual parameter is greater, or the actual parameter is smaller.
iii. State your conditions for accepting or rejecting the null hypothesis (that is, write them down)
You can do this either using the z-score or the t-value, or else by using the p value (obtained from a z-test or t-test, as appropriate, based on the sample and the assumed null.)
c. For either a or b, check the validity of using your method. This is a critical step for obtaining full credit, so I’m entering it as a separate post, next.</li>
</ol>
<p>This is 3.c, Check the validity of your method.
For example, if you are running a confidence interval or hypothesis test for the difference between two population parameters, you need to test four quantities:
n(sub 1) times p(sub 1) > 5
n(sub 1) times [1 - p(sub 1)] > 5
n(sub 2) times p(sub 2) > 5
and n(sub 2) times [1 - p(sub 2)] > 5</p>
<p>Not only that, but as far as we could tell from the scoring posted on the College Board site, you need to give the actual numerical values of n(sub 1) p(sub 1), n(sub 1) times [1 - p(sub 1)], n(sub 2) p(sub 2) and n(sub 2) [1 - p(sub 2)], no matter how totally obvious they are! Just stating that the inequalities are satisfied does not seem to gain you full credit–I think this may explain some of the bafflement of the Caltech-applicant, self-study crowd.</p>
<ol>
<li> This part is easy. Compute the result. You can use your calculator.</li>
</ol>
<p>Then, don’t forget to polish it off:
5. State your result as a conclusion in English. For example
“We can be confident at the 95% level that the true value of the difference between the mean price of Lindt chocolate and Ghiradelli chocolate in Peoria is between $0.37 per ounce and $0.54 per ounce.”
or
“We reject the hypothesis that Lindt chocolate and Ghiradelli chocolate are equally priced in Peoria, at the 95% confidence level.”</p>
<p>The graders tend to look for this as an indicator that you know what you are doing.</p>
<p>I hope this will all be helpful! It comes in the category of “answer-structuring” advice, as opposed to “how do I do this?” However, I think that following a structure like this will help you to gain the maximum possible points, given what you know.</p>
<p>Good guide. For people reading this, remember that in step 2, those aren’t the only conditions that must be met to perform most types of inferences, but it’s definitely a good starting point</p>
<p>Now that I’m getting into some serious review for AP Stat, any resource I can get my hands on is useful. So this is definitely appreciated. Are there any more tips that you could post? They’d be appreciated as well. I’m getting excited to take this exam. I just scored a 5 on a Barron’s practice exam :)</p>
<p>Yeah, Barron’s has questions that are typically more difficult than the actual AP exam. That’s why I’m especially excited about my progress. I took a released MC in class the other day and scored well enough to get a 5 as well, when added to my FRQ average from past FRQs. I only need a 4 to get out of Stats 221 at my college so I’m thinking I should be able to get that no problem. Looks like I’m shooting for a 5 now.</p>
<p>Quantmech, just a question: When answering a FRQ that’s not a hypothesis/inference test, such as a binomial/geometric probability question, can we just put what we do in the calculator, or do I have to actually write these formulas? I know I should write the probability statement but do I have to show calculations for z-score in a normalcdf problem if I can just do the whole thing in my calculator.</p>
<p>I don’t think you have to show the formula for the z-score. Someone please correct this if it’s wrong! You just have to say what you are doing, why it is valid, and what the result is (numerically and in words). With a binomial probability question, I probably would show the formula. Anyone know for sure whether you can omit it?</p>
<p>You must show formula for z-score, or else the response will be partially correct. With a binomial probability problem, you have to show calculation. If you plan to use a calculator, you must write down binomcdf(#,#,#) and identify the parameter for each of the number you input in binomcdf. </p>
<p>If you want to know how FR are graded or how responses should be worded, AP Central always have past FR and answer guidelines.</p>
<p>I thought you don’t need the formula for z-scores if it’s a normalcdf thing, but you need the formula for the test statistic when you are doing inference</p>