According to a recent study, when shopping online for luxury goods, men spend a mean of $ 2401 whereas women spend a mean of $ 1527. The study was based on a sample of 600 men and 700 women, and the standard deviation of the amount spent was $ 1200 for men and $ 1000 for women.
a) State the null and the alternative hypothesis if you want to determine whether the mean amount spent is higher for men than for women.
b) At the 0.01 level of significance, is there evidence that the mean amount spent is higher for men than for women?