Recall that “very satisfied” customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 65 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

a. Letting m represent the mean composite satisfaction rating for the XYZ- Box, set up the null hypothesis H0 and the alternative hypothesis Ha needed if we wish to attempt to provide evidence supporting the claim that m exceeds 42.

b. The random sample of 65 satisfaction ratings yields a sample mean of 42.954. Assuming that the population standard deviation equals 2.64, use critical values to test H0 versus Ha at each of α = .10, .05, .01, and .001.

c. Using the information in part b, calculate the p- value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001.

d. How much evidence is there that the mean composite satisfaction rating exceeds 42?