A car magazine is comparing the total repair costs incurred during the first three years on two sports cars, the T-999 and the XPY. Random samples of 45 T-999s and 51 XPYs are taken. All 96 cars are 3 years old and have similar mileages. The mean of repair costs for the 45 T-999 cars is $3300 for the first 3 years. For the 51 XPY cars, this mean is $3850. Assume that the standard deviations for the two populations are $800 and $1000, respectively.
a. Construct a 99% confidence interval for the difference between the two population means.
b. Using a 1% significance level, can you conclude that such mean repair costs are different for these two types of cars?
c. What would your decision be in part b if the probability of making a Type I error were zero? Explain.