Question

(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 709 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 4-7 237 174 411 8 - 13 84 74 158 14 - 21 55 90 22 or more 32 50 Total 374 335 709 35 18 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) 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.

Answer 1

Page No: Expeatted values. | Number of Nights. I pre 4-7 216.8 8 -13 83.3 14-21 47.5 22 or more. 26.4 Post 194.2 74.7 42.5 I 23.6 r² = scoig - Eijl? - Eis Eij o 237 2 16.8 ;;- Eij 20.2 0.7 1 -12 .5 84 35 4.4 83.3 47.5 26.4 194.2 74.7 42.5 23.6 Co jj- Eij) coi;-Eij) Eij 1 408.os 1 1. 88 21 0.49 ovo588 156.25 3.2895 70.56 2.6727 408.06 2.1011 0.49 0.0066 156.25 3.6765 70.56 1 2.9898 - 20.2 74 55 12.5 32 M = I long-6352 Eij [ 16.6242 df= (2-17 5S-1) = 14-1762-1) df. - 13

re ces critical value = Crititalrolne = 2²3, 0.01 30.0L - I 11.345 y critical value. (B-) we can reiect the hull hypo. that the length of stay is independent of retirement and acceer the alternative that the two variable are dependent # n=14, 12=8 Xx=74, y = 8.1. Fu= 83.1, su=7.34 Ho: Ha Mr = lu er <Mu df = nitn₂ - 2 - 14+8 -2 = 20 a les Test statisti, = D. nz When Sp= in,125,² + (n2-1352 mitna-2

= 137 65.61+ 20 7X53.88 852.93+377.16 20 sp= f 61.5045 Sp = 7.8425 t = 74-83. I 7. 8425 Lt 14 8 3.4758 t = -2.6181 - 2 6 181 Criticalralue = -1.725. i. We reject to The results are significant. The seem to indicates that people living in mural communities have a differnt. expenfancy than those in warba er have a differnt life those in verban Communiter.