AP Statistics Test Prep Table of Contents Part 1: Test OverviewSlide 2Slide 2 Part 2: Test...

AP Statistics Test PrepTable of ContentsPart 1: Test Overview Slide 2Part 2: Test Content Slide 4Part 3: 2013 Released Qs Slide 11Part 4: Specific Concepts Slide 21Part 5: Stats in a Nutshell Slide 26Part 6: Example Questions Slide 31Part 7: Formulas Slide 47Part 8: Calculator Shortcuts Slide 52Part 9: Study Guide by Chapter Slide 59

© Richard Newton 2013

AP Statistics Test Prep

Part 1: Test Overview

AP Stats Test is May 10th at Noon!AP Statistics Exam Study Materials!

Barron’s “AP Statistics”Princeton Review’s “Cracking the AP”Kaplan’s “5 Steps to a 5”

Part 1: Multiple Choice50% of overall Grade40 Questions90 Minutes

Part 2: Free Response50% of overall Grade6 Questions (5 and 1)90 Minutes

Breakdown:Each Multiple Choice Question is 1.25% of the overall scoreEach of the first 5 free response questions is 7.5% of the overall scoreThe final question is 12.5% of the overall score

There is no penalty for guessing.

AP Test Prep – Part 1: Test Overview


Part 2: Test Content

AP Test Prep – Part 2: Test ContentThe course can be divided into 4 major topics:

1. Exploratory Analysis2. Planning a Study3. Probability4. Inference

You will see 1 Free Response on each of these and 1 “Investigative Task” which is basically where you hit all of them in a single question.

Being able to look at a multiple choice or free response question and put it into 1 of these categories is one of the best skills you can learn.

Exploratory AnalysisCh.1) Categorical vs. Quantitative Data Types of Graphs Describe the Distribution: SOCSCh.2) Density Curves (Area = 1) Normal Curves z-scores (Percentiles) Testing Normal: 5 Number Summary Box Plot

Use histogram to check normal 68-95-99.7 Test Normal Probability PlotCh.3) LSRL (y = a + bx, r, r2, residual)Ch.4) Marginal Distributions Conditional Distributions Simpsons Paradox Exponential Regression Power Regression

- Look back at the various types of graphs and be familiar with which can be used with categorical vs. quantitative. You can expect to see at least 2 questions on stem plots – possibly with a back to back stem plot. You will see 2+ histograms as well. It is possible that you will see an O-give but unlikely you would have to convert it backward into a histogram.

- Make sure you can find the area under a density curve if it is blocky. They’ll likely ask you to check if a data set is normal.

- Make sure you’re able to create and interpret a LSRL line – in particular, refresh your memory on r, r2, and residuals!

- Marginal and Conditional Distributions just means you’re able to interpret 2 way tables and answer questions about the data.

AP Test Prep – Part 2: Test Content

Planning a StudyCh.5) Designing Observational Studies Stratified Random Sample Multistage Sampling Design Bias Voluntary Response Convenience Sampling Leading Question Non Response Bias Response Bias Designing Experiments Matched Pairs Block Design

Control and Placebo Simulations

- If you split your observational study up by strata, you are stratifying it.

- Be sure that you understand the specific types of bias!

“The design is biased if it systematically favors certain outcomes.”- If you have each participant experience both

treatments (1 after the other), you’ve used a Matched Pairs design. You could also attempt to match each participant with a very similar participant so that for each treatment, you have similar experimental units. This would be an attempt at a Matched Pairs design but I don’t think they’ll ask about this.

- Make sure you can diagram experiments, especially if they are blocked.

- Using a placebo is an attempt to create a control group to which you can compare your results.

- Use randomInt to conduct simulations.


ProbabilityCh.6) Probability And (*)vs. Or (+) Replacement without Replacement Disjoint (not overlapping) Non Disjoint (overlapping)Ch.7) Discrete (integer columns) Continuous z-scores Combining Means Combining VarianceCh.8) Binomial Distributions Geometric Distributions Permutations Combinations Counting Principal

- Remember the Bridge and Moat!- Most sequential probability questions are

done with replacement (unless it says otherwise).

- Diagram – tree or chart – probability questions wherever possible. Most can be reasoned out with a diagram and fractions alone.

- Remember that discrete involves integer columns which makes them easier to work with but that means > and ≥ are different.

- Continuous is composed of infinitely small columns and unless it’s rectangular or normal, you don’t have the tools to calculate the areas.

- BinomPDF is a single column while BinomCDF is a single column and all the columns to the left.


- The sampling distribution is normal because of the Central Limit theorem if the rules of thumb are met. This is the principal which allows us to calculate probabilities and estimate standard deviation.

ALWAYS: Talk about the conditions!!1) Is the SRS from the population of interest?2) How big is the sample size? Is that big

enough to do the test you’re doing?You will get marked off big time if you don’t!

- You will only see t tests (see chapter 11 middle board), prop tests (ch.12), chi-squared (ch.13), and LSRL tests (ch.14).

- You can do this entire part with a calculator and get full credit! Just check the conditions, explain the hypothesis, show the t score and probability, and then clearly state if the Null or Alternative is supported!

InferenceCh.9) Sampling Distributions Central Limit TheoremCh.10) Inferences when σ is known (z)

Type 1 Error Type 2 ErrorCh.11) Inferences when σ is unknown (t)Ch.12) Proportions 1propZtest 2propZtestCh.13) Chi-Squared GOF Chi-Squared HomogeneityCh.14) LSRL Significance TestConfidence Intervals:They ONLY want to see:1. The interval (either notation is fine)2. What the interval means“We are 95% confident the true mean (or proportion) is between ____ and ____.”


Other topics that are not tested:Covariance (combining variance when they are not independent)Baye’s TheoremPooled t-tests Chapter 14.2 – LSRL Confidence Intervals


Read the Question

Re-Read the Question

ExploratoryAnalysis

LSRL

Categorical vs. QuantitativeSOCSCenter vs. Spread

y a bx xy ab

10a by xDesigning Studies

Observational Studies vs. ExperimentsSimulations

ProbabilityMutual Exclusivity Independence vs. DependenceAnd vs. OrDiscrete vs. ContinuousBinomial vs. Geometric

Significance Tests and Confidence Intervals

Z-Tests vs. T-Tests Samples vs. ProportionsConfidence Intervals Chi-Squared LSRL


Part 3: 2013 Released Qs

At first I thought I had to do a 1propZinterval, but I realized since they gave me the mean mean and standard deviation of a single sample, I had to do a t-interval.

We are 95% confident that the true mean for lead levels in crows to be between 4.4157 and 5.3843 ppm

AP Test Prep – Part 3: 2013 Released Qs

Pop > 10n

Football game attendees might be more school spirited which might cause bias in the results and overestimate the proportion which are satisfied with the appearance of the university buildings and grounds.

Using the list of 70,000 names, assign each student a number from 1 to 70,000, then have the number generator generate 500 unique random numbers from 1-70,000. The students who match those numbers are selected for the survey.

At first I thought this was saying the campuses were gender specific, but both campuses are mixed.

If the campuses are different, such that the results of the survey when stratified by location is expected to give different results, then it would be important to survey each campus individually rather than by gender.


Simple z-score question.850 840

1.2667.9

xz

%100 89.8% 10.2%P

i) Combined mean = 840g840g – 20g for the carton = 820g for the dozen eggs, divided by 12 = 68.33 grams per egg

mean of X = 68.33gii) Combined standard deviation = 7.9g, so Combined variance = 62.41gContainer standard deviation = 1.7g, so variance = 2.89g 62.41 – 2.89 = 59.52g variance combined for 12 eggs 59.52 / 12 = 4.96g variance for a single egg 2.23g standard deviation for a single egg

standard deviation of X = 2.23g


Because we’re given a 2-way table, I know that I need to do a Chi-Squared Test of Homogeneity. I need to first generate my Expected values. You can see those below. Then I need to do a Chi-Squared Homogeneity T-test.

Yes, at a probability of 1.12% there is significant evidence at the 5% level to support the alternative hypothesis. There appears to be an association between age group and fruit/vegi consumption.

H0: No association between age and fruit/vegi consumption.Ha: There is an association between age and fruit/vegi consumption.


This is an observational study, meaning that treatments were not applied. Thus, lurking variables could be at work so we would not want to make any conclusions about causation.

If the situation were replicated and made into an experiment, control groups could be established to attempt to mitigate the impact of lurking variables. This would allow the researchers to make stronger conclusions about causation between meditation and blood pressure.


b) There are a few issues – #1, the sample size of 11 is too small, it should be atleast 15 #2, To do a matched pairs design like this and set the u of the differences to zero for the Null, you want to have the same sample size

Values over here indicate the proportion with high bp was higher for non meditators

Values over here indicate the proportion with high bp was higher for meditators

The simulated distribution favors the left side, where meditators have a lower proportion of individuals with high bp than non meditators. For this reason, it might be reasonable to conclude that there is a relationship between meditation and blood pressure.



Part 4: Specific Concepts

AP Test Prep – Part 4: Specific ConceptsThings that are important to remember:

Type 1 Error: Rejecting the Null when it’s actually true - P(type 1 error) = alphaType 2 Error: Accepting the Null when it’s actually false –

P(type 2 error) is difficult to calculate (and not on the test, thankfully)Power = 1 – P (type 2 error)

High power is good – it means you’re unlikely to commit a type 2 errorWays to increase power: increase sample size or move alternative further away

Simulation: If you’re asked to explain how you would simulate something, make sure you clearly identify what different number values will mean, example:RandomInt(1,10)1-3: Miss4-10: make10 trials, results are: 5, 3, 2, 8, 5, 10, 1, 1, 6, 7

4 misses, 6 makes Experimental Result = 40% miss rate

Repeated this process 5 times and got: 40%, 60%, 10%, 30%, 40% Mean Miss Rate after 5 trials of experiment: 36% miss rate

Any t-test will fall into one of these categories: Considerations:

1 Sample t test – Use Calculator, set μ = whatever was givenMatched Pairs – Use calculator (use 1 sample t test), set μ = zero2 Sample T test – Use calculator, set μ1 = μ2

1 prop Z test – Use calculator, set p = whatever was given2 prop Z test – Use calculator, set p1 = p2

X2 GOF – No shortcut in a TI83 - sum((L1-L2)2/L2)X2 Homogeneity – use calculator, Matrix A and B – df = (r-1)(c-1)

LSRL – Use Calculator, df = n - 2

SRS comes from population of interestN ≥ 15

SRS comes from population of interestPop ≥ 10nNp ≥ 10 or n(1-p) ≥10

SRS comes from population of interest

Observations are independentTrue relationship is linearS the same everywhereResiduals are normally distributed

AP Test Prep – Part 4: Specific Concepts

Confidence Intervals

The formula is always the same:

You can just use your calculator to calculate most of them. Just remember that df = n – 1 unless it’s LSRL and then its df = n – 2 (but you shouldn’t see a LSRL confidence interval).

Remember the definition of a confidence interval – it is very specific:

“If you conducted the sampling process multiple times and created many additional confidence intervals, 95% of the created intervals should contain the true mean.”

Or:“We are 95% confident that the true mean is between these two values.”

: *s

C x tn


Combining Means and Variances

Let’s say that you and your friend are ordering 2 items at a restaurant – a burrito and a chicken salad. You know that the following about the time (in minutes) it takes to make each item:

mean standard deviationBurrito 2 1Chicken Salad 3 2

Combined mean is:Combined standard deviation is:



Part 5: Stats in a Nutshell

AP Test Prep – Part 5: Stats in a Nutshell


Part 6: Example Questions

AP Test Prep – Part 6: Example Questions


Part 7: Formulas

AP Test Prep – Part 7: Formulas


Part 8: Calculator Shortcuts

AP Test Prep – Part 8: Calculator Shortcuts


Part 9: Study Guide by Chapter

AP Test Prep – Part 9: Study Guide by ChapterChapter 1 – Exploring Data

AP Test Prep – Part 9: Study Guide by ChapterChapter 2 – Normal Distributions – z scores

AP Test Prep – Part 9: Study Guide by ChapterChapter 3 – Examining Relationships - LSRL

AP Test Prep – Part 9: Study Guide by ChapterChapter 4 – 2 Variable Data

AP Test Prep – Part 9: Study Guide by ChapterChapter 5 – Producing Data

AP Test Prep – Part 9: Study Guide by ChapterChapter 5 continued – Producing Data

AP Test Prep – Part 9: Study Guide by ChapterChapter 6 - Probability

AP Test Prep – Part 9: Study Guide by ChapterChapter 7 – Random Variables

AP Test Prep – Part 9: Study Guide by ChapterChapter 8 – Binomial and Geometric Distributions

AP Test Prep – Part 9: Study Guide by ChapterChapter 9 – Sampling Distributions

AP Test Prep – Part 9: Study Guide by ChapterChapter 10 – Z Tests

AP Test Prep – Part 9: Study Guide by ChapterChapter 11 – T tests

AP Test Prep – Part 9: Study Guide by ChapterChapter 11 continued – T tests

AP Test Prep – Part 9: Study Guide by ChapterChapter 12 – Prop tests

AP Test Prep – Part 9: Study Guide by ChapterChapter 13 – Chi Squared

AP Test Prep – Part 9: Study Guide by ChapterChapter 14 – LSRL test

AP Statistics Test Prep Table of Contents Part 1: Test OverviewSlide 2Slide 2 Part 2: Test...

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