According to a recent study, when shopping online for luxury goods, men spend a

Question

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 60 men and 70 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 0.05 level of significance, is there evidence that the mean amount spent is higher for men than for women?

Explanation / Answer

a) H0: mean(men) = mean(women)
H1: mean(men) < mean(women)

b) first have to decide whether to pool variances (F test will show pooling appropriate)
sp^2=[(60-1)(1200)^2 + (70-1)(1000)^2]/(60+70-2) = 120,281.25 and sp=sqrt(120,281.25) = 1096.73

now test (2401-1527)/[1096.73sqrt(1/60 + 1/70)] = 4.53 and reject H0 and conclude men spend more than women, on average.

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