Question

1. (24 pts) 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 684 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 8- 13 14-21 22 or more Total 242 81 30 10 363 164 70 56 406 151 86 41 684 321 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 ? 0 .01 (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 hy pothesis that the length of stay is independent of retire- ment. . B. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alter native hypothesis that the two are dependent.

Could you please help me with this problem. Thank you!

Answer 1

Ho : length of stay and retirement are independent H length of stay and retirement are Not independent Pre-retirement Post-retireent Total 164 70 56 31 321 406 151 86 41 4 to 242 81 30 8 to 13 14 to 2130 10 363 22 or more Total (Row Total) (Column Total) We calculate expected frequencies by: E - Grand Total Col-1 Col-2 Row-1 Row-2 Row-3 406 363 684 151363 684 86 363 684 41 363 215.46 80.14 45.64 406 321 684 151 321 684 86 321 684 41 321 684 190.54 70.86 40.36 Row-4 19.24 бы -~ 21.76 To calculate chi-square test statistic we calculate this formula on each cell (Observed Count - Expected Count)2 Expected Count Observed Count Expected Count O - E)2

242 164 81 70 30 56 10 31 215.465 190.535 80.136 70.864 45.64 40.36 21.759 19.241 3.267868 3.695439 0.009316 0.010535 5.359744 6.061018 6.35462 7.186065 31.944 605 Test statistic: Y231.945 Significance level 0.01 Degrees of freedom ,df-(r -1)(c-1)-(4-1) (2-1) 3 Critical value: ..01-11.345 X201 has area of 0.01 to its right. To find X2.01 , open any Chi-square table, go across from ow df- v-3 and doum from column 0.01 and get 11.345 To get p-value, we can use excel function CHISQ.DIST.RT 31.944605, 3)5.3761 x 100.0000 Since test statistic is greater than critical value , we (reject null hypothesis. At 1% level, there is sufficient evidence that length of stay and retirement are not independent, i.e, that length of stay and retirement are significantly associated