7.82 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.

7.83 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.

7.84 Average hours per week on the Internet.

The Student Monitor surveys 1200 undergraduates from 100 colleges semiannually to understand trends among college students.³³ 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.

7.85 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.

7.86 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 0.0002 gram.

410

7.87 Credit card fees.

The bank in Exercise 7.30 (page 377) tested a new idea on a sample of 125 customers. Suppose that the bank wanted to be quite certain of detecting a mean increase of in the credit card amount charged, at the significance level. Perhaps a sample of only customers would accomplish this. Find the approximate power of the test with for the alternative as follows:

7.88 A field trial.

The tomato experts who carried out the field trial described in Exercise 7.39 (page 378) suspect that the relative lack of significance there is due to low power. They would like to be able to detect a mean difference in yields of 0.3 pound per plant at the 0.05 significance level. Based on the previous study, use 0.51 as an estimate of both the population and the value of in future samples.

7.89 Assessing noise levels in fitness classes.

In Exercise 7.53 (pages 394–395), you compared the noise levels in both high-intensity and low-intensity fitness classes. Suppose you are concerned with these results and want to see if the noise levels in high-intensity fitness classes in your city are above the “standard’’ level . You plan to take an SRS of classes in your neighborhood. Assuming , and the alternative mean is , what is the approximate power?

7.90 Comparison of packaging plants: power.

Exercise 7.55 (page 395) summarizes data on the number of seeds in one-pound scoops from two different packaging plants. Suppose that you are designing a new study for their next improvement effort. Based on information from the company, you want to identify a difference in these plants of 150 seeds. For planning purposes assume that you will have 20 scoops from each plant and that the common standard deviation is 190 seeds, a guess that is roughly the pooled sample standard deviation. If you use a pooled two-sample test with significance level 0.05, what is the power of the test for this design?

7.91 Power, continued.

Repeat the power calculation in the previous exercise for 25, 30, 35, and 40 scoops from each plant. Summarize your power study. A graph of the power against sample size will help.

7.92 Margins of error.

For each of the sample sizes considered in the previous two exercises, estimate the margin of error for the 95% confidence interval for the difference in seed counts. Display these results with a graph or a sketch.

7.93 Ego strength: power.

You want to compare the ego strengths of MBA students who plan to seek work at consulting firms and those who favor manufacturing firms. Based on the data from Exercise 7.63 (page 396), you will use for planning purposes. The pooled two-sample test with will be used to make the comparison. You judge a difference of 0.5 point to be of interest.

7.94 Learning Spanish.

Use the sign test to assess whether the intensive language training of Exercise 7.34 improves Spanish listening skills. State the hypotheses, give the -value using the binomial table (Table C), and report your conclusion.

7.95 Design of controls.

Apply the sign test to the data in Exercise 7.36 (page 378) to assess whether the subjects can complete a task with a right-hand thread significantly faster than with a left-hand thread.