Among the ANES unique group of people who simultaneously rate Christian Fundamentalists and atheists at 100 on the feeling thermometer, is there a difference between men and women with regard to how they score on the Traditionalism Index? Here are the raw data:

Men's scores: 7, 10, 12, 11, 9, 10, 13, 8, 7

Women's scores: 5, 6, 5, 8, 5, 4, 11, 8

Carry out a t-test by hand and explain your results.

(Show work)