A study of the effect of the gender of the tester on sex-role differentiation scores 16 in Manhattan gave a random sample of preschool children the Occupational Preference Test. Children were asked to give three choices of what they wanted to be when they grew up. Each occupation was rated on a scale from l (traditionally feminine) to 5 (traditionally masculine), and a child’s score was the mean of the three selections. When the tester was male, the 50 girls had x = 2.9 ands = 1.4, whereas when the tester was female, the 90 girls had x = 3.2 and s = 1.2. Show all steps of a test of the hypothesis that the population mean is the same for female and male testers, against the alternative that they differ. Report the P-value and interpret.