Hi, I have some questions regarding the following problem; Following exercise 3 , we asked a random sample of 19 university men to estimate how much...

Hi,

I have some questions regarding the following problem;

Following exercise 3 , we asked a random sample of 19 university men to estimate how much they spent on clothing in the last month. The data is {175,150,100,100,200,200,200,100,0,200,80,100,120,80, 25,50,100,30,60}. Test the hypothesis that the population mean-amounts spent on clothes are different for men and women. Use a significant level of 0.05 and 0.01. Assume that the distributions of amount spending are approximately Normal.

In the previous question, it was about money spent on clothing by women and it was asked to compute the 95% and 99% confidence interval. So for this problem, I did a two-tailed test as if they were unpaired. My null hypothesis was the mean for women = the mean for men (difference is 0) and the alternative hypothesis was the opposite (they do not equal). Then, I calculated tobs with the following formula;  where X1 is the mean for women and X2 the mean for men. With all the calculations, I got that for both significance level of 0.01 and 0.05, tobs is smaller than t critical. Now, I'm wondering if I might have been wrong from the beginning. However, I know the question does not involve a one-tailed test because it is only about if there is a difference. Also, it is unpaired because it does not concern two groups related such as grooms as brides. So can you help me with where I might be wrong? I just think my teacher would not have ask to test at both significance level if they give the same answer, so I pretty sure I've made a mistake somewhere, I just do not understand where.

Thank you,

Alexia