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2nd Semester Statistics Final Review - KEY1. In a random sample of 1,250 adult drivers, 450 said that they would cut their driving by 10 percent ifthis significantly helped the environment. Find a 95 percent confidence interval estimate of theproportion of adult drivers who are willing to cut their driving by 10 percent to help the environment.(A) .36 1.96(B) .36 1.96(C) .36 1.96(D) .36 1.96(E) .36 1.96(.10)(.36) 1,250 (.10)(.90)1,250(.10)(.90) 1,250 (.36)(.64)1,250 (.36)(.64)1,2502. A 2007 survey of 980 American drivers concluded that 38 percent of the driving population would bewilling to pay higher gas prices to protect the environment. Which of the following best describeswhat is meant by the poll having a margin of error of 3 percent? Hint: Create the confidenceinterval.(A) Three percent of those surveyed refused to participate in the poll.(B) It would not be unexpected for 3 percent of the population to readily agree to higher gas prices.(C) Between 343 and 402 of the 980 drivers responded that they would be willing to bay higher gasprices to protect the environment.(D) If a similar survey of 980 American drivers was taken weekly, a 3 percent change in each week’sresults would not be unexpected.(E) It is likely that between 35 percent and 41 percent of the driving population would be willing topay higher gas prices to protect the environment3. When leaving for school on an overcast morning, you make a judgment on the null hypothesis: Theweather will remain dry. What would the results be of Type I and Type II errors?(A) Type I error: get drenched. Type II error: needlessly carry around an umbrella.(B) Type I error: needlessly carry around an umbrella. Type II error: get drenched(C) Type I error: carry an umbrella, and it rains. Type II error: carry no umbrella, and no rain(D) Type I error: get drenched. Type II error: carry no umbrella, but weather remains dry.(E) Type I error: get drenched. Type II error: carry an umbrella, and it rains.4. An office manager believes that the percentage of employees arriving is even greater than thepreviously claimed 7 percent. She conducts a hypothesis test on a random 200 employee arrivalsand fins 23 punching in late. Is this strong evidence against the .07 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 .10.(E) There is insufficient information to reach a conclusion.

5. Which of the following is a true statement?(A) Tests of significance (hypothesis tests) are designed to measure the strength of evidenceagainst the null hypothesis.(B) A well-planned test of significance should result in a statement either that the null hypothesis istrue or that it is false.(C) The null hypothesis is one-sided and expressed using either or if there is interest indeviations in only one direction.(D) When a true parameter value is farther from the hypothesized value, it becomes easier toreject the alternative hypothesis.(E) Increasing the sample size makes it more difficult to conclude that an observed differencebetween observed and hypothesized values is significant.6. Two confidence interval estimates from the same sample are (72.2, 77.8) and (71.3, 78.7). Oneestimate is at the 95 percent level, and the other is at the 99 percent level. Which is which?(A) (72.2, 77.8) is the 95 percent level.(B) (72.2, 77.8) is the 99 percent level.(C) This question cannot be answered without knowing the sample size.(D) This question cannot be answered without knowing the sample standard deviation(E) This question cannot be answered without knowing both the sample size and standard deviation.7. A confidence interval estimate is determined from the summer earnings of an SRS of n students. Allother things being equal, which of the following will result in a smaller margin of error?(A) A greater confidence level(B) A larger sample standard deviation(C) A larger sample size(D) Accepting less precision(E) Introducing bias into sampling8. Should there be more restriction on handguns? In a 1995 pre-Columbine survey, 255 out of 1,020adults answered in the affirmative; in a 2000 post-Columbine survey, 352 out of 1,100 answeredaffirmatively. Establish a 90 percent confidence interval estimate of the difference between theproportions of adults in 1995 and 2000 who support more restrictions on handguns.(A) (.25-.32) 1.645 (.25).75)1,020(.25)(.75)(B) (.25-.32) 1.645((C) (.25-.32) 1.96 1,020(.25).75)1,020(.25)(.75)(D) (.25-.32) 1.96( 1,020(E) (.25-.32) 2.576( (.32)(.68) (.32).68)1,100 1,100) (.32)(.68) (.32).68) (.25)(.75) 1,0201,100 1,100 ) (.32).68) 1,100)

9. What is the probability of a Type II error when a hypothesis test is being conducted at the 5percent significance level (α .05)?(A) .05(B) .10(C) .90(D) .95(E) There is insufficient information to answer this question.10. Which of the following is a true statement?(A) The probability of a Type II error does not depend on the probability of a Type I error.(B) In conducting a hypothesis test, it is possible to simultaneously make both a Type I and Type IIerror.(C) A Type II error will result if one incorrectly assumes the data are normally distributed(D) Type I and II errors are caused by mistakes, however small, by the person conducting the test.(E) A Type I error is a conditional probability.11. An assembly line machine is supposed to turn out bowling balls with a diameter of 8.55 inches. Eachday an SRS of five balls are pulled and measured. If there mean diameter is under 8.35 inches orover 8.75 inches, the machinery is stopped and an engineer is called to make adjustments beforeproduction is resumed. The quality control procedure may be viewed as a hypothesis test withH0: 𝜇 8.55 and HA: 𝜇 8.55. What would a Type II error result in?(A) A warranted halt in production to adjust the machinery(B) An unnecessary stoppage of the production process(C) Continued production of wrong size bowling balls(D) Continued production of proper size bowling balls(E) Continued production of bowling balls that randomly are the right or wrong size12. In a random survey of 500 women, 315 said they would rather be poor and thin than rich and fat; in arandom survey of 400 men, 220 said they would rather be poor and thing than rich and fat. Is theresufficient evidence to show that the proportion of women who would rather be poor and thin thanrich and fat is greater than the proportion of men who would rather be poor and thin than rich andfat?(A) Because .63 .55 there is strong evidence that the proportion of women is greater than that ofmen.(B) Because .0075 .01 there is very strong evidence that the proportion of women is greater thanthe proportion of men.(C) Because .01 .3029 .05 there is strong evidence that the proportion of women is greater thanthat of men.(D) There is insufficient evidence that the proportion of women is greater than that of men.(E) There is sufficient information to determine whether the proportion of women is greater thanthat of men.

13. Two 95 percent confidence interval estimates are obtained: 1st (78.5, 84.5) and 2nd (80.3, 88.2).a. If the sample sizes are the same, which has the larger standard deviation?b. If the sample standard deviations are the same, which has the larger sample size?(A)(B)(C)(D)(E)a. 1st b. 1sta. 1stb. 2ndnda. 2b. 1sta. 2ndb. 2ndMore information is needed to answer these questions.14. Which of the following is a true statement?(A) The p-value of a test is the probability of obtaining a result as extreme as or more extreme thanthe one obtained, assuming the null hypothesis is true.(B) If the p-value for a test is .043, the probability that the null hypothesis is true is .043(C) When the null hypothesis is rejected, it is because it is not true.(D) The greater the p-value, the greater the evidence against the null hypothesis.(E) A very large p-value provides convincing evidence that the null hypothesis is true.15. Given and experiment H0: 𝜇 25 and HA: 𝜇 25, and a possible true population value of 26, which ofthe following increase with an increase in the sample size n?(A) The probability of a Type I error(B) The probability of a Type II error(C) The power of the test(D) The significance level 𝛼(E) 1 – power16. The claim is made that the average IQ of student at Lake Wobegon High School is greater than 100.To Test this, the principal gathers an SRS of 25 students and finds their mean IQ is 102 with astandard deviation of 8.3 What is the test statistics in performing a hypothesis test of H0:and HA: 𝜇 100?(A) T (B) T (C) T (D) T (E) T 102 1008.3102 1008.325 102 1008.324 102 100(8.3) 25102 100(8.3) 24𝜇 100

17. Which of the following statement is true?(A) If a population parameter is known, there is no reason to run a hypothesis test on that parameter.(B) The P-value can be negative or positive depending upon whether the sample statistic is less thanor greater than the claimed value of the population parameter in the null hypothesis.(C) The P-value is based on a specific test statistic, so it must be chosen before an experiment isconducted.(D) If a P-value is larger than a specified value , then the data are statistically significant at thatlevel.(E) The P-value is a probability calculated assuming that the alternative hypothesis is true.18. In a well-known basketball study, it was reported that Larry Bird hit a second free throw in 48 outof 53 attempts after the first free throw was missed, and hit a second free throw in 251 of 285attempts after the first free throw was made. Is there sufficient evidence to say that theprobability that Bird will make a second free throw is different depending on whether or not hemade the first free throw?(A) P .001 so this is very strong evidence that the probabilities are different.(B) P is between .001 and .01, so this is strong evidence that the probabilities are different.(C) P is between .01 and .05, so this is moderate evidence that the probabilities are different.(D) P is between .05 and .10, so there is some evidence that the probabilities are different.(E) P .10, so there is little or no evidence that the probabilities are different19. Before televised debates, a poll of 800 registered voters showed, 560 in favor of a particularcandidate: after the debates a poll of 600 voters showed 450 in favor of the candidate. Is theresufficient evidence that the candidate’s popularity has increased-what is the test statistic?.7 .75(A) z (.7)(1 .7) (.75)(1 .75) 800600(B) z (C) z (D) z (E) z .7 .75(.7214)(.2786) (.7214)(.2786 800600 .7 .75 800(.7)(1 .7) 600(.75)(1 .75).7 .75(.725)(1 .725)700 .7 .75 700(.725)(1 .725)

20. A manufacturer of heart-lung machines periodically checks a sample of its product and performs amajor recalibration if readings are sufficiently off target. Similarly, a rug factory periodicallychecks the sizes of its throw rugs coming off an assembly line and halts production if measurementsare sufficiently off target. In both situations, we have the null hypothesis that the productionequipment is performing satisfactorily. For each situation, which is the more serious concern, a TypeI or Type II error?(A) Machine producer: Type I error, carpet manufacturer: Type I error(B) Machine producer: Type I error, carpet manufacturer: Type II error(C) Machine producer: Type II error, carpet manufacturer: Type I error(D) Machine producer: Type II error, carpet manufacturer: Type II error(E) This is impossible to answer without making an expected value judgment between human life andaccurate throw rug sizes.21. Which of the following would result in the widest confidence interval?(A) Small sample size and 95 percent confidence(B) Small sample size and 99 percent confidence(C) Large sample size and 95 percent confidence(D) Large sample size and 99 percent confidence(E) This cannot be answered without knowing an appropriate standard deviation22. Suppose H0: p .6, HA: p .6, and against the alternative p .7, the power is .8. Which of thefollowing is a valid conclusion?(A) The probability of committing a Type I error is .1.(B) If p .7 is true, the probability of failing to reject H0 is .2.(C) The probability of committing a Type II error is .3.(D) All of the above are valid conclusions.(E) None of the above are valid conclusions.23. We are interested in the proportion p of people who drive pick-up trucks in a large city. Sevenpercent of a simple random sample of 760 people say they drive pick-ups. What is the midpoint for a99 percent confidence interval estimate of p?(A) .005(B) .495(C) .5(D) p(E) None of the above24. If all other variables remain constant, which of the following will not increase the power of ahypothesis test?(A) Increasing the sample size(B) Increasing the significance level(C) Increasing the probability of a Type II error(D) Decreased variability in the data(E) Increased distance between the true and the hypothesized parameter.

25. A company negotiator claims that only 35 percent of union members will support a strike, but a unionrepresentative believes the true percentage is greater and runs a hypothesis test at the 5 percentsignificance level. If 57 out of an SRS of 150 union members say they are willing to strike, what isthe test statistic?(A) z (B) z (C) z (D) z .38 .35 150(.35)(1 .35).38 .375 (150)(.38) (1 .38).38 .35(.35)(1 .35)150 .38 .35(.38)(1 .38)150 (E) z 1.96.38 .35 150(.35)(1 .35)26. Given that the power of a significance test against a particular alternative is 96 percent, which ofthe following is true?(A) The probability of mistakenly rejecting a true null hypothesis is less than 4 percent.(B) The probability of mistakenly rejecting a true null hypothesis is 4 percent.(C) The probability of mistakenly rejecting a true null hypothesis is greater than 4 percent.(D) The probability of mistakenly failing to reject a false null hypothesis is 4 percent.(E) The probability of mistakenly failing to