Stats: Modeling the World

1. Stats: Modeling the World Unit 5A Review

2. Things to know� What is a sampling distribution How to find means and standard deviations for sampling distributions (on formula sheet) How to calculate probabilities as it relates to the CLT What a confidence interval means and how it is computed What a confidence level means What the margin of error means How to compute a confidence interval How to use the ME to find a sample size How margin of errors change as the confidence changes What you can conclude from a CI and what you can�t. The difference between the null and alternate hypotheses How to conduct a hypothesis test What a p-value means How to describe a Type I Error, Type II Error, and the Power of the test

3. About the test 19 multiple choice 4 free response As always, budget your time wisely! Make sure you know how to use your calculator to find intervals, test statistics, and p-values.

4. #1 Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts an SRS of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary? a) .1469 b) .1977 c) .4207 d) .8023 e) .8531

5. #2 The average number of daily emergency room admissions at a hospital is 85 with a standard deviation of 37. In an SRS of 30 days, what is the probability that the mean number of daily emergency admissions is between 75 and 95? a) .1388 b) .2128 c) .4090 d) .5910 e) .9474

6. #3 A confidence interval estimate is determined from a SRS of n students. Which of the following will result in a smaller margin of error? I. A smaller confidence level II. A smaller sample size a) I only b) II only c) both I and II

7. #4 A survey was conducted to determine the percentage of high school students who planned to go to college. The results were stated as 82% with a margin of error of 5%. What is meant by +/- 5%? a) Five percent of the population were not surveyed. b) In the sample, the percentage of students who plan to go to college was between 77% and 87% c) The percentage of the entire population of students who plan to go to college is between 77% and 87% d) It is unlikely that the given sample proportion result would be obtained unless the true percentage was between 77% and 87% e) Between 77% and 87% of the population were surveyed.

8. #5 A USA Today �Lifeline� column reported that in a survey of 500 people, 39% said they watch their bread while it�s being toasted. Establish a 90% confidence interval estimate for the percentage of people who watch their bread being toasted. a) 39% +/- .078% b) 39% +/- 2.2% c) 39% +/- 2.8% d) 39% +/- 3.6% e) 39% +/- 4.3%

9. #6 A politician wants to know what percentage of the voters support her position on a hot issue. What size voter sample should be obtained to determine with 90% confidence the support level to within 4%? a) 21 b) 25 c) 423 d) 600 e) 1691

10. #7 Which of the following are true statements? I. Hypothesis tests are designed to measure the strength of the evidence against the null hypothesis. II. A well-planned test should result in a statement either that the null hypothesis is true or that it is false. III. The alternate hypothesis is one-sided if there is interest in deviations from the null hypothesis in only one direction. a) I and II b) I and III c) II and III d) I, II, and III e) None of the above

11. #8 A building inspector believes that the percentage of new construction with serious code violations may be even greater than the previously claimed 7%. She conducted a hypothesis test on 200 new homes and finds 23 with serious code violations. Is this strong evidence against the 7% claim? a) Yes, because the P-value is .0062 b) Yes, because the P-value is 2.5 c) No, because the P-value is only .0062 d) No, because the P-value is over 2 e) No, because the P-value is .045

12. #9 Which is true about a 99% confidence interval based on a given sample? I. The interval contains 99% of the population. II. Results from approximately 99% of all samples will capture the true parameter in their respective intervals. III. The interval is wider than a 95% confidence interval would be. a) I only b) II only c) III only d) II and III only e) None

13. #10 A researcher investigating whether runners are less likely to get colds than non-runners found a P-value of 3%. This means that: a) 3% of runners get colds. b) 3% fewer runners get colds. c) There�s a 3% chance that runners get fewer colds. d) There's a 3% chance our assumption of no difference in number of colds whether a runner or not is incorrect. e) There�s a 3% chance that the sample statistic or more extreme will occur assuming there is no difference between number of colds whether a runner or not.

14. #11 In a SRS of 300 elderly men, 65% were married, while in an independent SRS of 400 elderly women, 48% were married. Determine a 99% confidence interval estimate for the difference between the percentages of elderly men and women who are married. a. 17% +/- 0.36% b. 17% +/- 9.6% c. 55% +/- 6.7% d. 56.5% +/- 6.7% e. 56.5% +/- 9.6%

15. #12 In leaving for school on an overcast April morning you make a judgment on the null hypothesis: The weather will remain dry. What would the results by of Type I and Type II errors? a. Type I: get drenched; Type II: needlessly carry around an umbrella. b. Type I: needlessly carry around an umbrella; Type II: get drenched. c. Type I: carry an umbrella and it rains; Type II: carry no umbrella, but weather remains dry. d. Type I: get drenched; Type II: carry no umbrella, but weather remains dry. e. Type I: get drenched; Type II: carry an umbrella and it rains.

16. Answers to MC 1. A 2. C 3. A 4. D 5. D 6. C B A D E B B