The mean of the sample of 65 customer satisfaction ratings in Table 1.7 is 42.95. If we let m denote the mean of all possible customer satisfaction ratings for the XYZ Box video game system, and assume that the population standard deviation equals 2.64:
a. Calculate 95 percent and 99 percent confidence intervals for μ.
b. Using the 95 percent confidence interval, can we be 95 percent confident that m is at least 42 (recall that a very satisfied customer gives a rating of at least 42)? Explain.
c. Using the 99 percent confidence interval, can we be 99 percent confident that m is at least 42? Explain.
d. Based on your answers to parts b and c, how convinced are you that the mean satisfaction rating is at least 42?