AP Statistics Name:_________________________________ Test – 1 and 2 sample-proportions Sampling Distributions, Confidence Intervals, and Hypothesis Testing Part 1: Multiple-Choice 1. A random sample has been taken from a population. A statistician, using this sample, needs to decide whether to construct a 90% confidence interval or a 95% confidence interval to estimate the population proportion. How will these intervals differ? (A) (B) (C) (D) (E) 2. A survey to estimate the mean length of time people had lived in a certain community was conducted by calling land-line telephones and asking, "How long have you lived in Pleasant Valley?" Those conducting the survey are concerned about the possibility of under-coverage, since some people do not own a phone or own only a cell phone. Which of the following is the best way for them to correct for this source of bias? (A) (B) (C) (D) (E) 3. The 90 percent confidence interval will be wider that the 95 percent confidence interval The 90 percent confidence interval will not be as wide as the 95 percent confidence interval Which interval is wider will depend upon how large the sample was. Which interval is wider will depend upon whether the sample was unbiased. There is insufficient information available to answer the question. Use a lower confidence level, such as 80%. Use a higher confidence level, such as 99%. Take a larger sample. Eat some pie and go home. Throw this sample out and start over again with a better sampling method. A researcher is suddenly granted extra money for her study and realizes that she can increase the size of her sample from 100 to 400. If she decides to do this, what will happen to the size of her confidence interval? (A) It will be divided by 2 (D) It will be multiplied by 4 4. (B) It will be multiplied by 2 (E) It will remain unchanged. (C) It will be divided by 4 A well-conducted poll showed that in a sample of 1500 potential voters 46% intend to vote for I. M. Sleazy for governor. The poll had a reported margin of error of 3%. Which of the following best describes what is meant by “margin of error”? (A) (B) (C) (D) (E) The probability is 0.97 that between 43% and 49% of the voters will vote for candidate Sleazy. Ninety-seven percent of the time, between 43% and 49% of the voters wouldvote for candidate Sleazy. The proportion of voters who will vote for candidate Sleazy is most likely to be between 43% and 49%. Three percent of those interviewed refused to answer the question. Between 43% and 49% of the voters will vote for candidate Sleazy. 5. In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the U.S. Supreme Court. A claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the U.S. Supreme Court. Which of the following best represents the null and alternate hypotheses? (A) Ho: p = .50; Ha: p = .43 (B) Ho: p = .50; Ha: p ≠ .50 (C) Ho: ̂ = .43; Ha: ̂ < .50 (D) Ho: p = .50; Ha: p < .50 (E) Ho: ̂ = .50; Ha: ̂ < .50 6. In a national survey of 2013 adults, 1283 indicated that they believe rudeness is a more serious problem than in years past. Which confidence interval gives an estimate of the true proportion of adults who think that rudeness is a more serious problem than in years past with 99% confidence? (A) (B) (C) (D) (E) Not enough information 7. Which of the following are true statements? I. The p-value of a test is the probability of obtaining a result as extreme (or more extreme) as the one obtained assuming the null hypothesis is true. II. If the p-value for a test is .015, the probability that the null hypothesis is true is .015. III. When the null hypothesis is rejected, it is because it is not true. (A) I only (B) II only (C) III only (D) I and III (E) None of the above gives the complete set of true responses #8-9 refer to the following scenario: A building inspector believes that the percentage of new construction with serious code violations may be even greater than the previously claimed 7%. She conducts a hypothesis test on 200 new homes and finds 23 with serious code violations. 8. What are the null and alternate hypotheses for this situation? (A) Ho: p = .07; Ha: p > .07 (B) Ho: ̂ = .115; Ha: ̂ > .115 (D) Ho: p = .07; Ha: p > .115 (E) Ho: p = .07; Ha: p ≠ .07 (C) Ho: ̂ = .07; Ha: ̂ > .07 9. Is the inspector’s evidence against the .07 claim strong? (A) No, because the p-value is only .0063. (B) No, because the p-value is over 2.0. (C) No, because the p-value is .045 (D) Yes, because the p-value is .0063. (E) Yes, because the p-value is 2.49. 10. A restaurant owner claims that only 15% of visiting tourists stay for more than 2 days. A chamber of commerce volunteer is sure that the real percentage is higher. He plans to survey 100 tourists and intends to speak up if at least 18 of the tourists stay longer than 2 days. What is the probability of mistakenly rejecting the restaurant owner’s claim if it is true? (drawing a pic might help) (A) .8402 (B) .2367 (C) .2004 (D) .1728 (E) .4010 11. A 1993 Los Angeles Times poll of 1703 adults revealed that only 17% thought the media was doing a “very good” job. Which represents the best level of confidence the newspaper should use to say that 17% 2.5% of adults believe the media is doing a “very good” job? (A) 73% (B) 90% (C) 95% (D) 97% (E) 99% 12. It is believed that 82% of high school students believe everything they read and hear on the internet. In a random sample of 50,000 high school students across the nation, what is the probability that, um, no? (circle all that apply) (A) I. hate. you. (B) Gorillas (C) 5.23 x 10-7 (D) 1 (E) π Fill in the blank: 13. The Associated Press found that 462 of 1000 randomly selected adults preferred to watch movies at home rather than at a movie theater. Is there convincing evidence that the majority of adult Americans prefer watching movies at a theater? p = ____________________________________________________________________________________________________ Ho: _________ Ha: _________ z = _________ p-value = _________ What do you conclude? 14. In a survey of 526 U.S. businesses, 383 indicated that they monitor employee’s web site visits. Is there sufficient evidence that more than 70% of U.S. businesses monitor employees’ web site visits? p = ____________________________________________________________________________________________________ Ho: _________ Ha: _________ What do you conclude? z = _________ p-value = _________ Part II – Show all work and answers in a neat and orderly fashion. 15. I want to estimate the proportion of my students that sleep less than what experts recommend each night (8 hours) with 90% confidence and a margin of error of +3.5%. (a) How many students do I need to survey in order to remain (b) I want to increase the confidence level to 95% now. What within these constraints? sample size do I need in order to keep the same margin of error? c) Suppose that 5th block rolls around and I forgot to take the time to survey other classes throughout the day. My 5 th block AP Statistics class is 10 students. What confidence level should I choose to keep my margin of error to +3.5%? d) Describe two things that make statistically illegal for me to ask you to do part c. 18. Ho: All systems are operating satisfactorily with regard to a NASA shuttle launch 19. Most people know Aesop’s fable “The Boy Who Cried Wolf” about a shepherd boy who repeatedly tricks nearby villagers into thinking a wolf is attacking his flock. When a wolf actually does appear, the villagers do not believe the boy's cries for help, and the flock is destroyed. Explain what a Type I error would be in this context. Explain how this fable relates to a Type I error. Explain what a Type II error would be in this context. Explain how this fable relates to a Type II error. Which error is more severe and why? 17. A study of teenage suicide included a random sample of 96 boys and 123 girls between ages of 12 and 16 years selected scientifically from admissions records to a private psychiatric hospital. Suicide attempts were reported by 18 of the boys and 60 of the girls. Construct a 95% confidence interval to estimate the difference between the two proportions. 18. Based on your interval, does it appear that girls are more likely to attempt suicide at this age than boys? Justify your answer. 19. Two competing drugs are available for treating a specific ailment. There are no apparent side effects from drug #1, whereas there are (nausea and headache) from drug #2. A group of researchers have decided however that they are willing to recommend drug #2 if the proportion of cures for the second drug are higher than the proportion for the first drug. The researchers use the drugs experimentally on two groups of people who are suffering from the ailment. By the end of the experiment, 52 out of 80 treated with drug #1 were classified as cured, whereas 63 out of 90 who were given drug #2 are so classified. At the 1% significance level, should the second drug be recommended? 20. If your conclusion is erroneous, explain what type of error was committed. What consequences will result from this error?