CHAPTER 7 Review Exercises 365 7. Requirements A construction quality control analyst has collected a random sample of six concrete road barriers, and she plans to weigh each of them and construct a 95% confidence interval estimate of the mean weight of all such barriers. What requirements must be satisfied in order to construct the confidence interval with the method from Section 7-2 that uses the t distribution? 8.Degrees of Freedom In general, what does “degrees of freedom” refer to? For the sample data described in Exercise 7 “Requirements,” find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of m using the t distribution. 9.Critical Value Refer to Exercise 7 “Requirements” and assume that the requirements are satisfied. Find the critical value that would be used for constructing a 95% confidence interval estimate of m using the t distribution. 10.Which Method? Refer to Exercise 7 “Requirements” and assume that sample of six weights appears to be from a population having a distribution that is substantially far from being normal. Should a 95% confidence interval estimate of s be constructed using the x2 distribution? If not, what other method could be used to find a 95% confidence interval estimate of s? 1. Bachelor’s Degree in Four Years In a study of government financial aid for college students, it becomes necessary to estimate the percentage of full-time college students who earn a bachelor’s degree in four years or less. Find the sample size needed to estimate that percentage. Use a 0.1 margin of error, and use a confidence level of 95%. a. Assume that nothing is known about the percentage to be estimated. b. Assume that prior studies have shown that about 40% of full-time students earn bachelor’s degrees in four years or less. c. Does the added knowledge in part (b) have much of an effect on the sample size? 2.Bachelor’s Degree The president of Brown University wants to estimate the mean time (years) it takes students to earn a bachelor’s degree. How many students must be surveyed in order to be 95% confident that the estimate is within 0.2 year of the true population mean? Assume that the population standard deviation is s = 1.3years. 3.Voting Survey In a survey of 1002 people, 70% said that they voted in a recent presidential election (based on data from ICR Research Group). Voting records show that 61% of eligible voters actually did vote. a. Among the 1002 people surveyed, what is the actual number of people who said that they voted? b. Find a 95% confidence interval estimate of the percentage of people who say that they voted. c. Fill in the blanks for this statement that a typical reporter might write: Based on a survey, _____ percent of those surveyed say that they voted in the presidential election, and the survey has a margin of error of __________. d. Are the survey results consistent with the actual voter turnout of 61%? Why or why not? 4.Space Mountain Use the following wait times (minutes) for the Space Mountain ride at Disney World (from Data Set 33 “Disney World Wait Times” in Appendix B). Construct a 95% confidence interval estimate of the mean of all wait times. Write a brief statement that interprets that confidence interval. 40 35 40 40 25 80 50 30 35 40 5. Distributions Identify the distribution (normal, Student t, chi-square) that should be used in each of the following situations. If none of the three distributions can be used, what other method could be used? Review Exercises continued
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