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Name: __________________________ Date: _____________ INSTRUCTIONS: ANSWERS AS CURRENTLY GRADED ARE HIGHLIGHTED IN YELLOW ACCEPTABLE/CORRECTED ANSWERS ARE HIGHLIGHTED IN GREEN Question numbers and answer choices may not be necessarily in the same order as presented to you on the test. PLEASE USE YOUR SCAVENGER HUNT SKILLS! Use the following to answer question 1: The college newspaper of a large Midwestern university periodically conducts a survey of students on campus to determine the attitude on campus concerning issues of interest. Pictures of the students interviewed, along with quotes of their responses, are printed in the paper. Students are interviewed by a reporter “roaming” the campus who selects students to interview “haphazardly.” On a particular day the reporter interviews five students and asks them if they feel there is adequate student parking on campus. ˆ Four of the students say no. The sample proportion p that respond “no” is thus 0.8. ˆ 1. Referring to the information above, the standard error of p is A) 0.8. B) 0.64. C) 0.4. D) 0.18. E) 0.032. Use the following to answer question 2: ˆ A radio talk show host with a large audience is interested in the proportion p of adults in his listening area that think the drinking age should be lowered to 18. To find out, he poses the following question to his listeners: “Do you think that the drinking age should be reduced to 18 in light of the fact that 18-year-olds are eligible for military service?” He asks listeners to phone in and vote “yes” if they agree the drinking age should be lowered and “no” if not. 2. Of the 100 people who phoned in, 70 answered “yes.” Which of the following assumptions for inference about a proportion using a confidence interval are violated? A) The desired confidence level is not given. B) The population is at least 10 times as large as the sample. ˆ C) n is so large that both the count of successes np and the count of failures n(1 – p )ˆ are 10 or more. D) There appear to be no violations. E) The data are an SRS from the population of interest. 3. Eighty rats whose mothers were exposed to high levels of tobacco smoke during pregnancy were put through a simple maze. The maze required the rats to make a choice between going left or going right at the outset. Sixty of the rats went right when running the maze for the first time. Assume that the 80 rats can be considered an SRS from the population all rats born to mothers exposed to high levels of tobacco smoke during pregnancy. (Note that this assumption may or may not be reasonable, but researchers often assume lab rats are representative of such larger populations since lab rats are often bred to have very uniform characteristics.) The standard error for the sample ˆ proportion p of rats who went right the first time when running the maze is A) 0.0023. B) 0.0484. C) 0.0548. D) 0.0559. E) 0.4337. Page 1 Use the following to answer questions 4-5: A newspaper conducted a statewide survey concerning the 1998 race for state senator. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 620 would vote for the Republican candidate. Let p represent the proportion of registered voters in the state that would vote for the Republican candidate. 4. Referring to the information above, a 90% confidence interval for p is A) 0.517 ± 0.014. B) 0.517 ± 0.022. C) 0.517 ± 0.024. D) 0.517 ± 0.028. E) 0.517 ± 0.249. 5. Referring to the information above, what sample size would you need in order to estimate p with margin of error 0.01 with 95% confidence? Use the guess p = 0.5 as the value for p. A) 49. B) 1500. C) 4800. D) 4900. E) 9604. Use the following to answer questions 6-7: A noted psychic was tested for ESP. The psychic was presented with 200 cards face down and asked to determine if the card featured one of five symbols: star, cross, circle, square, or three wavy lines. The psychic was correct in 50 cases. Let p represent the probability that the psychic correctly identifies the symbol on the card in a random trial. 6. Referring to the information above, and assuming that the 200 trials can be treated as an SRS from the population of all guesses the psychic would make in his lifetime a 95% confidence interval for p is A) 0.25 ± 0.069. B) 0.25 ± 0.060. C) 0.25 ± 0.055. D) 0.25 ± 0.050. E) We can assert that p = 0.20 with 100% confidence because the psychic is just guessing. 7. Referring to the information above, suppose you wished to see if there is evidence that the psychic is doing better than if he were just guessing. To do this, you test the hypotheses H0: p = 0.20, Ha: p > 0.20. The P-value of your test is A) Greater than 0.10. B) Between 0.05 and 0.10. C) Between 0.01 and 0.05. D) Between 0.001 and 0.01. E) Below 0.001. Page 2 8. A newspaper conducted a statewide survey concerning the 1998 race for governor. The newspaper took a random sample (assume it is an SRS) of 1200 registered voters and found that 640 would vote for the Democratic candidate. Is this evidence that a clear majority of the population would vote for the Democratic candidate? To answer this, test the hypotheses H0: p = 0.50, Ha: p > 0.50. The P-value of your test is A) 0.4920. B) 0.0330. C) 0.0209. D) 0.0104. E) less than 0.0002. 9. An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. She intends to compute a 95% confidence interval for p. To do so, she selects an SRS of 50 potatoes from a shipment of over 2000 potatoes on a truck. Suppose that only two of the potatoes sampled are found to have major defects. Which of the following assumptions for inference about a proportion using a confidence interval are violated? A) n is so large that both np0 < 10 and n(1 – p0) < 10. ˆ ˆ B) n is so large that both the count of successes np and the count of failures n(1 – p ) are 10 or more. C) The population size is too small. D) The population is at least 10 times as large as the sample. E) There appear to be no violations. Use the following to answer question 10: After a college's football team once again lost a football game to the college's arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach. 10. Referring to the information above, a 95% confidence interval for p is A) 0.64 ± 0.009. B) 0.64 ± 0.079. C) 0.64 ± 0.094. D) 0.64 ± 0.124. E) 0.64 ± 0.360. Use the following to answer questions 11-12: An SRS of size 100 is taken from a population having proportion 0.8 of successes. An independent SRS of size 400 is taken from a population having proportion 0.5 of successes. 11. Referring to the information above, the sampling distribution for the difference in the ˆ ˆ sample proportions, p1 – p2 , has mean A) Equal to the smaller of 0.8 and 0.5. B) 0.56. C) 0.3. D) 0.15. E) The mean cannot be determined without knowing the sample results. Page 3 12. Referring to the information above, the sampling distribution for the difference in the ˆ ˆ sample proportions, p1 – p2 , has standard deviation A) 1.3. B) 0.40. C) 0.047. D) 0.055. E) 0.002. 13. An SRS of 100 of a certain popular model car in 1993 found that 20 had a certain minor defect in the brakes. An SRS of 400 of this model car in 1994 found that 50 had the minor defect in the brakes. Let p1 and p2 be the proportion of all cars of this model in 1993 and 1994, respectively, that actually contain the defect. A 90% confidence interval for p1 – p2 is 0.075 ± 0.071. Suppose the sample of 1993 cars consisted of only 10 cars, of which two had the minor brake defect. Suppose also the sample of 1994 cars consisted of only 40 cars, of which five had the minor brake defect. A 90% confidence interval for p1 – p2 is now A) the same as that for the original sample of 100 and 400 cars. B) much wider than that for the original sample of 100 and 400 cars. C) the same as 99% for the original sample of 100 and 400 cars. D) unsafe to compute, since it is unsafe to use the normal distribution to approximate the sampling distribution of E) much narrower than that for the original sample of 100 and 400 cars. Use the following to answer question 14: In a large Midwestern university (with the class of entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in 1993 found that 20 finished in the bottom third of their high school class. Admission standards at the university were tightened in 1995. In 1997, an SRS of 100 entering freshmen found that 10 finished in the bottom third of their high school class. Let p1 be the proportion of all entering freshmen in 1993 who graduated in the bottom third of their high school class, and let p2 be the proportion of all entering freshmen in 1997 who graduated in the bottom third of their high school class. 14. Referring to the information above, is there evidence that the proportion of freshmen who graduated in the bottom third of their high school class in 1997 has been reduced as a result of the tougher admission standards adopted in 1995, compared to the proportion in 1993? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 > p2. The P- value of your test is A) Greater than 0.10. B) Between 0.05 and 0.10. C) Between 0.01 and 0.05. D) Between 0.001 and 0.01. E) Below 0.001. 15. A manufacturer receives parts independently from two suppliers. An SRS of 400 parts from supplier 1 finds 20 defectives. An SRS of 100 parts from supplier 2 finds 10 defectives. Let p1 and p2 be the proportions of all parts from suppliers 1 and 2, respectively, that are defective. A 95% confidence interval for p1 – p2 is A) –0.05 ± 0.063. B) –0.05 ± 0.053. C) –0.05 ± 0.052. D) –0.05 ± 0.032. E) 0.05 ± 0.032. Page 4 Use the following to answer question 16: An SRS of 100 flights by Airline 1 showed that 64 were on time. An SRS of 100 flights by Airline 2 showed that 80 were on time. Let p1 be the proportion of on-time flights for all Airline 1 flights, and let p2 be the proportion of all on-time flights for all Airline 2 flights. 16. Referring to the information above, a 95% confidence interval for the difference p1 – p2 is A) –0.16 ± 0.062. B) –0.16 ± 0.122. C) –0.16 ± 0.104. D) –0.16 ± 0.103. E) 0.16 ± 0.062. Use the following to answer questions 17-18: An agricultural researcher wishes to see if a kelp extract helps prevent frost damage on tomato plants. Two similar small plots are planted with the same variety of tomato. Plants in both plots are treated identically, except that the plants on plot 1 are sprayed weekly with a kelp extract, while the plants on plot 2 are not. After the first frost in the autumn, the percentage of damaged fruit is determined. For plants in plot 1, 20 of the 100 tomatoes on the vine exhibited damage. For plants in plot 2, 36 of the 100 tomatoes on the vine showed damage. Let p1 be the actual proportion of all tomatoes of this variety that would experience crop damage under the kelp treatment, and let p2 be the actual proportion of all tomatoes of this variety that would experience crop damage under the no-kelp treatment, assuming that the tomatoes are grown under conditions similar to those in the experiment. 17. Referring to the information above, a 99% confidence interval for p1 – p2 is A) –0.16 ± 0.062. B) –0.16 ± 0.122. C) –0.16 ± 0.161. D) 0.16 ± 0.062. E) 0.16 ± 0.161. 18. Referring to the information above, is there evidence of a decrease in the proportion of tomatoes suffering frost damage for tomatoes sprayed with kelp extract? To determine this, you test the hypotheses H0: p1 = p2, Ha: p1 < p2. The P-value of your test is A) Greater than 0.10. B) Between 0.05 and 0.10. C) Between 0.01 and 0.05. D) Between 0.001 and 0.01. E) Below 0.001. Use the following to answer question 19: An SRS of 25 male faculty members at a large university found that 10 felt that the university was supportive of female and minority faculty. An independent SRS of 20 female faculty found that five felt that the university was supportive of female and minority faculty. Let p1 represent the proportion of all male faculty members at the university and p2 represent the proportion of all female faculty members at the university who hold the stated opinion. Page 5 19. Referring to the information above, a 95% confidence interval for p1 – p2 is A) 0.15 ± 0.355. B) 0.15 ± 0.270. C) 0.15 ± 0.227. D) 0.15 ± 0.138. E) 0.15 ± 0.168. Use the following to answer question 20: A sociologist is studying the effect of having children within the first three years of marriage on the divorce rate. From city marriage records, she selects a random sample of 400 couples that were married between 1985 and 1990 for the first time, with both members of the couple being between the ages of 20 and 25. Of the 400 couples, 220 had at least one child within the first three years of marriage. Of the couples that had children, 83 were divorced within five years, while of the couples that didn't have children, only 52 were divorced within three years. Suppose p1 is the proportion of couples married in this time frame that had a child within the first three years and were divorced within five years and p2 is the proportion of couples married in this time frame that did not have a child within the first two years and were divorced within five years. 20. Referring to the information above, the estimate of p1 – p2 is A) 0.0775. B) 0.0884. C) 0.3100. D) 0.3375. E) 0.3773. Page 6