Chapter 9 & 10 Review Name Multiple Choice. 1. An agricultural researcher plants 25 plots with a new variety of corn. The average yield for these plots is X = 150 bushels per acre. Assume that the yield per acre for the new variety of corn follows a normal distribution with unknown mean µ and standard deviation σ = 10 bushels. A 90% confidence interval for µ is A) 150 ± 2.00. B) 150 ± 3.29. C) 150 ± 3.92. D) 150 ± 16.45. E) 150 ± 32.90. 2. An agricultural researcher plants 25 plots with a new variety of corn. A 90% confidence interval for the average yield for these plots is found to be 162.72 ± 4.47 bushels per acre. Which of the following would produce a confidence interval with a smaller margin of error than this 90% confidence interval? A) Choosing a sample with a larger standard deviation. B) Planting 100 plots, rather than 25. C) Choosing a sample with a smaller standard deviation. D) Planting only 5 plots, rather than 25. E) None of the above. 3. The heights of young American women are normally distributed with mean µ and standard deviation σ = 2.4 inches. If I want the margin of error for a 99% confidence interval for µ to be ± 1 inch, I should select a simple random sample of size A) 2. B) 7. C) 16. D) 38. E) 39. 4. Researchers are studying the yield of a crop in two locations. The researchers are going to compute independent 90% confidence intervals for the mean yield µ at each location. The probability that at least one of the intervals will cover the true mean yield at its location is A) 0.19. B) 0.81. C) 0.90. D) 0.95. E) 0.99. 5. Scores on the Math SAT (SAT-M) are believed to be normally distributed with mean µ. The scores of a random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for µ based on these data is A) 550.00 ± 173.88. D) 550.00 ± 105.01. B) 550.00 ± 142.00. E) 550.00 ± 79.21. C) 550.00 ± 128.58.
6. A phone-in poll conducted by a newspaper reported that 73% of those who called in liked business tycoon Donald Trump. The number 73% is a A) statistic B) sample C) parameter D) population E) census 7. If a statistic used to estimate a parameter is such that the mean of its sampling distribution is equal to the true value of the parameter being estimated, the statistic is said to be A) random B) biased C) a proportion D) unbiased E) normal 8. The heights (in inches) of males in the United States are believed to be normally distributed with mean µ. The average height of a random sample of 25 American adult males is found to be X = 69.72 inches, and the standard deviation of the 25 heights is found to be s = 4.15 inches. The standard error of X is A) 0.17. B) 0.41. C) 0.69. D) 0.83. E) 2.04. 9. To estimate the mean salary µ of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is X = $73,220 and the sample standard deviation is s = $4400. A 99% confidence interval for µ is A) 73,220 ± 11,440. B) 73,220 ± 572. C) 73,220 ± 5567. D) 73,220 ± 431. E) 73,220 ± 28.6. 10. The variability of a statistic is described by A) the spread of its sampling distribution B) the amount of bias present C) the vagueness in the wording of the question used to collect the sample data D) the stability of the population it describes 11. A fair coin is tossed 60 times. The probability that less than 1/3 of the tosses are heads is A) 0.33 B) 0.109 C) 0.09 D) 0.0031 E) 0 12. A random sample X has mean µ x and standard deviation! x. Suppose n independent observations of X are taken and the average x of these n observations is computed. We can assert that if n is large, the sampling distribution of x is approximately normal. This assertion follows from A) the law of large numbers B) the CLT (central limit theorem) C) the definition of sampling distribution D) the bell curve
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. 13. 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. 14. 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. 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. Four of the students say no. The sample proportion ˆp that respond no is thus 0.8. 15. Referring to the information above, the standard error of ˆp is A) 0.8. B) 0.64. C) 0.4. D) 0.18. E) 0.032. 16. Referring to the information above, which of the following assumptions for inference about a proportion using a confidence interval are violated in this example? A) n is so large that both ˆ np and n(1 - ˆp ) are at least 10. B) The population is at least 10 times as large as the sample. C) We are interested in inference about a proportion. D) The data are an SRS from the population of interest. E) There appear to be no violations. 17. A sociologist is studying the effect of having children within the first two years of marriage on the divorce rate. Using hospital birth records, she selects a random sample of 200 couples that had a child within the first two years of marriage. Following up on these couples, she finds that 80 are divorced within five years. A 90% confidence interval for the proportion p of all couples that had a child within the first two years of marriage and are divorced within five years is A) 0.40 ± 0.004. B) 0.40 ± 0.035. C) 0.40 ± 0.044. D) 0.40 ± 0.057. E) 0.40 ± 0.068.
18. Suppose the manufacturer of official NFL footballs uses a machine to inflate the new balls to a pressure of 13.5 lbs. When the machine is properly calibrated, the mean inflation pressure is 13.5 lbs, but uncontrollable factors cause pressures of individual footballs to vary randomly from about 13.3 to 13.7 lbs, with " = 0.1. For quality control purposes, the manufacturer wishes to estimate the mean inflation pressure to within 0.025 pounds of its true value with a 99% confidence interval. What sample size should be specified for the experiment? 19. According to the June 1994 issue of Bicycling, only 16% of all bicyclists own helmets. You wish to conduct a survey in Newton to determine what percent of the bicyclists own helmets. Find the necessary sample size if you want your estimate to be within 0.02 with 90% confidence. Use.16 as your estimate for p.
Answers: 1. B 2. B 3. E 4. E 5. A 6. A 7. D 8. D 9. B 10. A 11. D 12. B 13. C 14. E 15. D 16. A 17. D 18. n = 107 19. n = 910