Recently the operations manager was concerned that calls were taking too long

A telemarketing company located in Los Angeles has established a guideline stating that the average time for each completed call should be no more than 4 minutes.

Recently the operations manager was concerned that calls were taking too long. The operations manager did not wish to assert that the calls were taking too long if the sample data did not strongly indicate this. A sample of 12 calls was selected and the following times (in seconds) were recorded.

194 278 302 140 245 234 268 208 302 190 320 255

a. Construct the appropriate null and alternative hypotheses.

b. Based on the sample data, what should the operations manager conclude? Test at the 0.10 significance level using the p-value approach. (Assume that call times are normally distributed.)

c. Suppose you wished to conduct the test in part b using X as the test statistic.

Calculate the critical value of X .

d. Consider your answer to part c. What values of the population mean could have been specified in the null hypothesis so that you would not reject the null hypothesis?