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Section 7.1 Exercises

7.2    You want to rent an unfumished one-bedroom apartment for next semester. You take a random sample of 10 apartments advertised in the local newspaper and record the rental rates. Here are the rents (in dollars per month):

500, 650, 600, 505, 450, 550, 515, 495, 650, 395

Find a 95% confidence interval for the mean monthly rent for unfumished one-bedroom apartments available for rent in this community.

7.3    If you chose 99% rather than 95% confidence, would your margin of error in the previous exercise be larger or smaller? Explain your answer and verify it by doing the calculations.

7.4    A random sample of 10 one-bedroom apartments from your local newspaper has these monthly rents (dollars):

500, 650, 600, 505, 450, 550, 515, 495, 650, 395

Do these data give good reason to believe that the mean rent of a11 advertised apartments is greater than $500 per month? State hypotheses, find the t statistic and its P-value, and State your conclusion.

7.5    A test of a nuli hypothesis versus a two-sided altemative gives t — 2.55.

(a)    The sample size is 25. Is the test result significant at the 5% level?

Explain how you obtained your answer.

(b)    The sample size is 5. Is the test result significant at the 5% level? What generał fact about statistical tests do your two ans wers illustrate?

7.6    You will have complete sales information for last month in a week but right now you have data from a random sample of 50 Stores. The mean change in sales in the sample is +4.8% and the standard deviation of the changes is 15%. Are average sales for all Stores different from last month?

(a)    State appropriate nuli and altemative hypotheses. Explain how you decided between the one- and two-sided altematives.

(b)    Find the t statistic and its P-value. State your conclusion.

(c)    If the test gives strong evidence against the nuli hypothesis, would you conclude that sales are up in every one of your Stores? Explain your answer.

7.7    You are using software to calculate t procedures for a large sample, n greater than 5000.

(a)    For a two-sided test, how large must the t statistic be to reach significance at the 1% level? (Notę that either a large positive number or a large negative number will be significant.)

(b)    In which row of Table D did you find your result in part (a)? What generał fact about the t distributions does this illustrate?

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