Refer to Exercise 7.87.

(a) Perform a test with the intention of establishing that the mean time to return a call is greater than 1.5 hours. Use \(\alpha=0.05\).

(b) In light of your conclusion in part (a), what error could you have made? Explain in the context of this problem.

(c) In a long series of repeated experiments, with new random samples collected for each experiment, what proportion of the resulting tests would reject the null hypothesis if it prevailed? Explain your reasoning.

Data From Exercise 7.87

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7.87 An industrial engineer concerned with service at a large medical clinic recorded the duration of time from the time a patient called until a doctor or nurse re- turned the call. A sample of size 180 calls had a mean of 1.65 hours and a standard deviation of 0.82. (a) Obtain a 95% confidence interval for the popula- tion mean of time to return a call. (b) Does lie in your interval obtained in part (a)? Explain. (c) In a long series or repeated experiments, with new random samples collected for each experi- ment, what proportion of the resulting confidence intervals will contain the true population mean? Explain your reasoning.