Math 227 Fall 2023 Classwork Nov. 3 NAME Hypothesis Testing for a Population Mean: Gender and Household Responsibilities In a society where men and women are equal, the various household responsibilities equally rest on both graders. Unfortunately, women usually carry the brunt of household work as well as the task of unpaid care for family members. In the United States the burden of care for pre-school age children as well as disabled family members and the elderly falls on the immediate family. There are few state funded pre-schools in the United States. The care for disabled and the elderly depends on whether there is an adequate health/ disability insurance and retirement planning. One way to determine who bears the brunt of the unpaid care is to determine the number of hours (say per week) spent on unpaid care work. EXAMPLE: Suppose in a region, men spend on average one hour per week on unpaid care work. Do women in the same region spend more time per week on unpaid care work. In a random sample of 49 women the mean time for unpaid work was 13 hours and the standard deviation of 0.4 hours, Test the claim that women spend more time on unpaid care work than men at 5% level of significance. What is the random variable