In Germany, there is a significant pay gap between men and women even after adjusting for the job and worker qualifications. Terre Des Femmes sent transgender individuals once as a man, and once as a woman, to interview for the same job. They developed nearly identical resumes for the pair (tweaked so that the two resumes were not identical) and recorded the starting salary offers in Euros. The following table reflects what Terre Des Femmes found as the starting salary offers for each individual - as a man and as a woman - in thousands of Euros. Assume that the differences are normally distributed. What is the p-value of the test of the hypothesis that men are offered a higher starting salary than a woman even if the man and the woman are actually the same person? Write your answer in decimals, not percent, (so 0.032 rather than 3.2%), and round your answer to three decimal places.
Starting salaries in Euros
able[[Individual,As a man,As a woman],[1,37.2,36],[2,27.6,21.6],[3,43.4,31.2]]