According to a recent study, when shopping online for luxury goods, men spend a mean of $2,401, whereas women spend a mean of $1,527. (Data extracted from R. A. Smith, "Fashion Online: Retailers Tackle the Gender Gap," TheWall Street Journal, March 13, 2008, pp. D1, D10.) Suppose that the study was based on a sample of 600 men and 700 females, and the standard deviation of the amount spent was $1,200 for men and $1,000 for women.
a. State the null and alternative hypothesis if you want to determine whether the mean amount spent is higher for men than for women.
b. In the context of this study, what is the meaning of the Type I error?
c. In the context of this study, what is the meaning of the Type II error?
d. At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women?