Unit V review

V-1 AP Statistics Test A – Inference for Proportions – Part V Name ____________________ __ 1. We have calculated a 95% confidence interval and would prefer for our next confidence interval to have a smaller margin of error without losing any confidence. In order to do this, we can I. change the z * value to a smaller number. II. take a larger sample. III. take a smaller sample. A) I only B) II only C) III only D) I and II E) I and III __ 2. Which is true about a 98% confidence interval for a population proportion based on a given sample? I. We are 98% confident that other sample proportions will be in our interval. II. There is a 98% chance that our interval contains the population proportion. III. The interval is wider than a 95% confidence interval would be. A) None B) I only C) II only D) III only E) I and II __ 3. We have calculated a confidence interval based on a sample of size n = 100. Now we want to get a better estimate with a margin of error that is only one-fourth as large. How large does our new sample need to be? A) 25 B) 50 C) 200 D) 400 E) 1600 __ 4. A certain population is bimodal. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one? I. The distribution of our sample data will be more clearly bimodal. II. The sampling distribution of the sample means will be approximately normal. III. The variability of the sample means will be smaller. A) I only B) II only C) III only D) II and III E) I, II, and III __ 5. The manager of an orchard expects about 70% of his apples to exceed the weight requirement for “Grade A” designation. At least how many apples must he sample to be 90% confident of estimating the true proportion within ± 4%? A) 19 B) 23 C) 89 D) 356 E) 505 __ 6. A P -value indicates A) the probability that the null hypothesis is true. B) the probability that the alternative hypothesis is true. C) the probability the null is true given the observed statistic. D) the probability of the observed statistic given that the null hypothesis is true. E) the probability of the observed statistic given that the alternative hypothesis is true.

V-2 __ 7. A statistics professor wants to see if more than 80% of her students enjoyed taking her class. At the end of the term, she takes a random sample of students from her large class and asks, in an anonymous survey, if the students enjoyed taking her class. Which set of hypotheses should she test? A) H H 0 A : . : . p p < > 0 80 0 80 B) H H A 0 0 80 0 80 : . : . p p = > C) H H 0 A : . : . p p > = 0 80 0 80 D) H H 0 A : . : . p p < ≠ 0 80 0 80 E) H H 0 A : . : . p p = < 0 80 0 80 __ 8. Not wanting to risk poor sales for a new soda flavor, a company decides to run one more taste test on potential customers, this time requiring a higher approval rating than they had for earlier tests. This higher standard of proof will increase I. the risk of Type I error II. the risk of Type II error III. power A) I only B) II only C) III only D) I and II E) I and III __ 9. Suppose that a manufacturer is testing one of its machines to make sure that the machine is producing more than 97% good parts H and H 0 A : . : . p p = > ( ) 0 97 0 97 . The test results in a P -value of 0.122. Unknown to the manufacturer, the machine is actually producing 99% good parts. What probably happens as a result of the testing? A) They correctly fail to reject H 0 . B) They correctly reject H 0 . C) They reject H 0 , making a Type I error. D) They fail to reject H 0 , making a Type I error. E) They fail to reject H 0 , making a Type II error. __10. Which of the following is true about Type I and Type II errors? I. Type I errors are always worse than Type II errors. II. The severity of Type I and Type II errors depends on the situation being tested. III. In any given situation, the higher the risk of Type I error, the lower the risk of Type II error. A) I only B) II only C) III only D) I and III E) II and III 11. Approval rating The President’s job approval rating is always a hot topic. Your local paper conducts a poll of 100 randomly selected adults to determine the President’s job approval rating. A CNN/ USA Today /Gallup poll conducts a poll of 1010 randomly selected adults. Which poll is more likely to report that the President’s approval rating is below 50%, assuming that his actual approval rating is 54%? Explain.

V-4 14. Internet access A recent Gallup poll found that 28% of U.S. teens aged 13-17 have a computer with Internet access in their rooms. The poll was based on a random sample of 1028 teens and reported a margin of error of ±3%. What level of confidence did Gallup use for this poll? 15. Sleep Do more than 50% of U.S. adults feel they get enough sleep? According to Gallup’s December 2004 Lifestyle poll, 55% of U.S. adults said that that they get enough sleep. The poll was based on a random sample of 1003 U.S. adults. Test an appropriate hypothesis and state your conclusion in the context of the problem.