A marketing manager wishes to compare the mean prices charged for two brands of CD players. The manager conducts a random survey of retail outlets and obtains independent random samples of prices. The six retail outlets at which prices for the Onkyo CD player are obtained have a mean price of $ 189 with a standard deviation of $ 12. The twelve retail outlets at which prices for the JVC CD player are obtained have a mean price of $ 145 with a standard deviation of $ 10. Assuming normality and equal variances:
a. Use an appropriate hypothesis test to determine whether the mean prices for the two brands differ. How much evidence is there that the mean prices differ?
b. Use an appropriate 95 percent confidence interval to estimate the difference between the mean prices of the two brands of CD players. Do you think that the difference has practical importance?
c. Use an appropriate hypothesis test to provide evidence supporting the claim that the mean price of the Onkyo CD player is more than $ 30 higher than the mean price for the JVC CD player. Set α equal to .05.