These are my questions and please give detailed explanation. Thanks a lot !

1. Suppose that a company wishes to examine the relationship of gender to job satisfaction, grouping job satisfaction into four categories: very satisfied, somewhat satisfied, somewhat dissatisfied and very dissatisfied. The company plans to ask the opinion of 100 employees. Should you, the company statistician, carry out a Chi-squared test of independence or a test of homogeneity?3. Dowdall {1974) studied the effect of ethnic background on role attitude of women ages 1564 in Rhode Island. Respondents were asked whether they though it was all right for a woman to have a job instead of taking care of the house and children while her husha nd worked. The following table breaks down the response by ethnic origin of the respondent. Is there a relationship between response and ethnic group? Ethnic Origin Yes No -_ French 42 23 Portuguese 29 7 5. Let X1, X2, ."., Xn be independent random variables following a normal distribution, each with a different mean /; but with common variance o?; that is: Xi~ N(uj, 02) for i = 1,2, ..., n. Let X denote X = _ Show that for i = 1,2, ..., n: Cov(X;, X) = n