Recall that \"very satisfied\" customers give the XYZ-Box videogame system a rating that is at least 42. Suppose that themanufacturer of the XYZ-Box wishes to use the random sample of 68satisfaction ratings to provide evidence supporting the claim thatthe mean composite satisfaction rating for the XYZ-Box exceeds 42.(a) Letting µ represent the mean composite satisfaction rating forthe XYZ-Box, set up the null hypothesis H0 and the alternativehypothesis Ha needed if we wish to attempt to provide evidencesupporting the claim that µ exceeds 42. H0: µ 42 versus Ha: µ 42.(b) The random sample of 68 satisfaction ratings yields a samplemean of x⎯⎯=42.810. Assuming that σ equals 2.70, use criticalvalues to test H0 versus Ha at each of α = .10, .05, .01, and .001.(Round your answer z.05 to 3 decimal places and other z-scores to 2decimal places.) z = Rejection points z.10 z.05 z.01 z.001 RejectH0 with α = , but not with α = (c) Using the information in part(b), calculate the p-value and use it to test H0 versus Ha at eachof α = .10, .05, .01, and .001. (Round your answers to 4 decimalplaces.) p-value = Since p-value = is less than ; reject H0 atthose levels of α but not with α = . (d) How much evidence is therethat the mean composite satisfaction rating exceeds 42? There isevidence.
