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(1 point) It has been suggusted that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre- and post-retirees. A sample of 704 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below. Number of Nights Preretirement Postretirement 4 7 241 165 8 13 80 74 14 21 40 51 22 or more 19 34 53 Total 380 324 704 With this information, construct a table of estimated expected values. Number of Nights Pre-retirement Post-retirement 4 7 8 13 14 21 22 or more Now, with that information, determine whether the length of stay is independent of retirement using a = 0.05. (a) 12 = (b) Find the degrees of freedom: (c) The final conclusion is CA. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent. O B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement. (1 point) The number of men and women among professors in Math, Physics, Chemistry, Linguistics, and English departments from a SRS of small colleges were counted. and the results are shown in the table below. Dept. Math Physics Chemistry Linguistics English Men 51 106 46 33 47 Women 6 5 9 2O 30 Test the claim that the gender of a professor is independent of the department. Use the significance level a = 0.025 (a) The test statistic is ,'(2 = (b) Is there sufficient evidence to warrant the rejection of the claim that the gender of a professor is independent of the department? A. No Q B. Yes