14. please show all work for this problem and round as far as possible

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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 693 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below. Number of Nights Pre-retirement Post-retirement Total 4-7 249 161 410 8-13 84 62 146 14-21 31 57 88 22 or more 14 35 49 Total 378 315 693 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 =0.01. (a) Find test value x2 (b) Find the degrees of freedom: (c) Find the critical value: (d) The final conclusion is A. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement. B. 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.