AP Stat Review

1. Descriptive Statistics Probability Inferential Statistics Experimental Design Conditions Grab Bag AP Stat Review

2. 100 points If the mean of a distribution is greater than its median, what is most likely the shape of the distribution? Skewed right

3. 200 points If the range of a set of data is 36, what is a reasonable estimate of the standard deviation? 6

4. 300 points If the test scores of a class of 30 students have a mean of 75.6 and the test scores of another class of 24 students have a mean of 68.4, then the mean of the combined group is… 72.4

5. 400 points Joey scored a 720 on the math portion of the SAT and Luke scored a 34 on the math portion of the ACT. Scores for each test are Normally distributed. The SAT has a mean of 580 and a standard deviation of 100, while the ACT has a mean of 26 with a standard deviation of 5. Who had the better relative performance? Luke

6. 500 points • For a particular bivariate data set, r2 is found to be 0.64. Interpret this value. 64% of the variation in y can be accounted for by least squares regression of y on x.

7. 100 points When do we say that the design of a study is biased? When certain outcomes are systematically favored.

8. 200 points What is the difference between an observational study and an experiment? In an experiment, a treatment is applied.

9. 300 points A research team wishes to compare performance in AP Statistics based on whether the students were taught using activity-based or traditional lecture methods. The final grades in AP Statistics for 500 students were collected. What is the population of interest? All students taking AP Statistics

10. 400 points Name four components for a valid controlled experiment. Control, comparison, replication, and randomization

11. 500 points What is the purpose of a control group in an experiment? To control the effect of lurking variables and to reduce bias

12. 100 points A company claims that the number of defective items manufactured during each run of making 100 of their products is independent of the number from other runs and that the proportion of defectives is no more than 4%. Assume that the proportion of defectives for each run is .04. What is the probability that there will be no defectives on the next run? 0.017

13. 200 points The number of sweatshirts a vendor sells daily has the following probability distribution: If each sweatshirt sells for $25, what is the expected daily total dollar amount taken in by the vendor from the sale of sweatshirts? $38

14. 300 points In a certain game, a fair die is rolled and a player gains 20 points if the die shows a “6.” If the die does not show a “6,” the player loses 3 points. If the die were to be rolled 100 times, what would be the expected total gain or loss for the player? About 83

15. 400 points All bags entering a research facility are screened. Ninety-seven percent of the bags that contain forbidden material trigger an alarm. Fifteen percent of the bags that do not contain forbidden material also trigger the alarm. If 1 out of every 1,000 bags entering the building contains forbidden material, what is the probability that a bag that triggers the alarm will actually contain forbidden material? 0.00643

16. 500 points A student is taking a 5 question multiple choice test. Each question has 4 choices of answers. If a student randomly answers the questions find the probability that the student answers at least 4 questions correctly. 0.015625

17. 100 points A P-value of a test of significance is the probability that… A sample of this size will produce a statistic this or more extreme if the null hypothesis is true.

18. 200 points Correct this statement: if the P-value of a test is greater than α, we accept the null hypothesis. We fail to reject the hull hypothesis

19. 300 points What is a type I error? We reject the null hypothesis when we should not have.

20. 400 points Name two way we can reduce the width of a confidence interval? Increase sample size; reduce the confidence level

21. 500 points A local news station reports that the 97% confidence interval for a candidate’s support was (43%, 48%). What does the phrase 97% confidence mean? If we repeated this procedure many times, 97% of the resulting CI’s would contain the true population proportion.

22. 100 points List the conditions for a one-sample z-test. SRS; Normality; Independence; σ is known.

23. 200 points Name the conditions for a one-proportion z-test. SRS; np ≥ 10 and n(1 – p) ≥ 10; population > 10*sample

24. 300 points Name the conditions for Chi-square GOF test. SRS; All expected counts ≥ 1; No more than 20% of expected counts < 5

25. 400 points How do we show Normality for a t-test? Stated; n > 30 (CLT); n > 15 with no clear outliers (CLT); n < 15 with no skewness or outliers (CLT)

26. 500 points What do we say if a condition is not met? Continue with the test, but we have concerns over the results.

27. 100 points What is z* for a 95% confidence interval? 1.96

28. 200 points What is t* for a 90% confidence interval for a sample size of 30? 1.7011

29. 300 points A large company is considering opening a franchise in St. Louis and wants to estimate the mean household income for the area using a simple random sample of households. Based on information from a pilot study, the company assumes that the standard deviation of household incomes is σ = $7,200. Of the following, which is the least number of households that should be surveyed to obtain an estimate that is within $200 of the true mean household income with 95% confidence? About 5000 (4978)

30. 400 points Name two ways of increasing the power of a test. Increase sample size, increase alpha, decrease standard deviation

31. 500 points How can we tell if a residual plot reveals a linear pattern? Random scatter, no patterns