One of the top-selling video games continues to be Mad-den NFL 12. While prices vary widely depending on store or website, the suggested retail price for this video game is $59.95. The file titled Madden contains a random sample of the retail prices paid for Madden NFL 12.
a. Calculate the sample mean and standard deviation of retail prices paid for Madden NFL 12.
b. To determine if the average retail price has fallen, assume the population mean is $59.95, calculate the probability that a sample of size 200 would result in a sample mean no larger than the one calculated in part a. Assume that the sample standard deviation is representative of the population standard deviation.
c. In part b, you used $59.95 as the population mean. Calculate the probability required in part b assuming that the population mean is $59.50.
d. On the basis of your calculations in parts b and c, does it seem likely that the average retail price for Madden NFL 12 has decreased? Explain.