7.101 What is wrong? In each of the following situations, identify what is wrong, and then either explain why it is wrong or change the wording of the statement to make it true.

7.102 Apartment rental rates. You hope to rent an unfurnished one-bedroom apartment in Dallas next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having taken a statistics course recently, the friend asks about the desired margin of error and confidence level for this estimate. He also tells you that the standard deviation of monthly rents for one-bedrooms is about $300.

7.103 More on apartment rental rates. Refer to the previous exercise. Will the 95% confidence interval include approximately 95% of the rents of all unfurnished one-bedroom apartments in this area? Explain why or why not.

7.104 Average hours per week on the Internet. The Student Monitor surveys 1200 undergraduates from 100 colleges semiannually to understand trends among college students.⁴³ Recently, the Student Monitor reported that the average amount of time spent per week on the Internet was 19.0 hours. You suspect that this amount is far too small for your campus and plan a survey.

7.105 Average hours per week listening to the radio. Refer to the previous exercise. The Student Monitor also reported that the average amount of time listening to the radio was 11.5 hours.

7.106 Accuracy of a laboratory scale. To assess the accuracy of a laboratory scale, a standard weight known to weigh 10 grams is weighed repeatedly. The scale readings are Normally distributed with unknown mean (this mean is 10 grams if the scale has no bias). The standard deviation of the scale readings in the past has been 0.0013 gram.

7.107 Accuracy of a laboratory scale, continued. Refer to the previous exercise. Suppose that instead of a confidence interval, the researchers want to perform a test (with α = 0.05) that the scale is unbiased (μ = 10).

7.108 Sample size calculations. You are designing a study to test the null hypothesis that μ = 0 versus the alternative that μ is positive. Assume that σ is 20. Suppose that it would be important to be able to detect the alternative μ = 4. What sample size is needed to detect this alternative with power of at least 0.80?

7.109 Power of the comparison of DXA machine operators. Suppose that the bone researchers in Exercise 7.45 (page 431) want to be able to detect an alternative mean difference of 0.002. Find the power for this alternative for a sample size of 20 patients. Make sure to explain the reasoning of your choice of standard deviation in these calculations.

7.110 Determining the sample size. Consider Example 7.23 (page 465). What is the minimum sample size needed for the power to be greater than 80% when μ = 14.5?

7.111 Changing the significance level. In Example 7.24 (page 468), we assessed the power of a new study of calcium on blood pressure assuming n₁ = n₂ = 45 subjects. The power was based on α = 0.01. Suppose that we wanted to use α = 0.05 instead.

7.112 Planning a study to compare tree size. In Exercise 7.79 (page 459), DBH data for longleaf pine trees in two parts of the Wade Tract are compared. Suppose that you are planning a similar study in which you will measure the diameters of longleaf pine trees. Based on Exercise 7.79, you are willing to assume that the standard deviation for both halves is 20 cm. Suppose that a difference in mean DBH of 10 cm or more would be important to detect. You will use a t statistic and a two-sided alternative for the comparison.

7.113 More on planning a study to compare tree size. Refer to the previous exercise. Find the two standard deviations from Exercise 7.79. Do the same for the data in Exercise 7.80 (page 459), which is a similar setting. These are somewhat smaller than the assumed value that you used in the previous exercise. Explain why it is generally a better idea to assume a standard deviation that is larger than you expect than one that is smaller. Repeat the power calculations for some other reasonable values of σ and comment on the impact of the size of σ for planning the new study.

7.114 Planning a study to compare ad placement. Refer to Exercise 7.78 (page 458), where we compared trustworthiness ratings for ads from two different publications. Suppose that you are planning a similar study using two different publications that are not expected to show the differences seen when comparing the Wall Street Journal with the National Enquirer. You would like to detect a difference of 1.5 points using a two-sided significance test with a 5% level of significance. Based on Exercise 7.78, it is reasonable to use 1.6 as the value of the common standard deviation for planning purposes.

7.115 Sign test for potential insurance fraud. The differences in the repair estimates in Exercise 7.40 (page 430) can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you obtained in Exercise 7.40?

7.116 Sign test for the comparison of operators. The differences in the TBBMC measures in Exercise 7.45 (pages 431–432) can also be analyzed using a sign test. Set up the appropriate null and alternative hypotheses, carry out the test, and summarize the results. How do these results compare with those that you obtained in Exercise 7.45?

7.117 Sign test for fuel efficiency comparison. Use the sign test to assess whether the computer calculates a higher mpg than the driver in Exercise 7.41 (pages 430–431). State the hypotheses, give the P-value using the binomial table (Table C), and report your conclusion.

7.118 Insulation study. A manufacturer of electric motors tests insulation at a high temperature (250̊ C) and records the number of hours until the insulation fails.⁴⁴ The data for five specimens are

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The small sample size makes judgment from the data difficult, but engineering experience suggests that the logarithm of the failure time will have a Normal distribution. Take the logarithms of the five observations and use t procedures to give a 90% confidence interval for the mean of the log failure time for insulation of this type.