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Chapter 8: Q 77. (page 543)
Estimating BMI The body mass index (BMI) of all American young
women is believed to follow a Normal distribution with a standard deviation of about . How large a sample would be needed to estimate the mean BMI μ in this population to within with confidence?
Sample size is.
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Critical values What critical value from Table B should be used for a confidence interval for the population mean in each of the following situations?
a. A confidence interval based on randomly selected observations
b. A confidence interval from an SRS of observations
c. A confidence interval based on a random sample of size
Running red lights A random digit dialing telephone survey of 880 drivers asked, “Recalling the last ten traffic lights you drove through, how many of them were red when you entered the intersections?” Of the 880 respondents, 171 admitted that at least one light had been red.37
a. Construct and interpret a 95% confidence interval for the population proportion.
b. Nonresponse is a practical problem for this survey—only 21.6% of calls that reached a live person were completed. Another practical problem is that people may not give truthful answers. What is the likely direction of the bias: Do you think more or fewer than 171 of the 880 respondents really ran a red light? Why? Are these sources of bias included in the margin of error?
Reading scores in Atlanta The Trial Urban District Assessment (TUDA) is a
government-sponsored study of student achievement in large urban school districts. TUDA gives a reading test scored from to . A score of is a “basic” reading level and a score of is “proficient.” Scores for a random sample of eighth-graders in Atlanta had a mean of with standard deviation of
a. Construct and interpret a confidence interval for the mean reading test score of all Atlanta eighth-graders.
b. Based on your interval from part (a), is there convincing evidence that the mean reading test score for all Atlanta eighth-graders is less than the basic level? Explain your answer.
The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favor the proposal, Of these, 89 say "Yes."
a. Construct and interpret a confidence interval for the proportion of all visitors to Yellowstone who favor the restrictions.
b. Based on your work in part (a), is there convincing evidence that more than half of all visitors to Yellowstone National Park favor the proposal? Justify your answer.
More cheating Refer to Exercise 36. Calculate and interpret the standard error of for these data.
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