A telephone company claims that the mean duration of all long-distance phone calls made by its residential customers is 10 minutes. A random sample of 100 long-distance calls made by its residential customers taken from the records of this company showed that the mean duration of calls for this sample is 9.20 minutes. The population standard deviation is known to be 3.80 minutes.
a. Find the p-value for the test that the mean duration of all long-distance calls made by residential customers of this company is different from 10 minutes. If α = .02, based on this p-value, would you reject the null hypothesis? Explain. What if α = .05?
b. Test the hypothesis of part a using the critical-value approach and α = .02. Does your conclusion change if α = .05?