Question

(2 points) 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 701 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 4-7 247 172 8- 13 75 62 137 14 - 21 40 51 9 1 22 or more 14 40 Total 376 325 With this information, construct a table of estimated expected values. Number of Nights Pre-retirement Post-retirement 47 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 (b) Find the degrees of freedom:

Answer 1

Date: 11/11/2019 Answer The expected values table is, By using Excel software, find expected values with the help of following steps: 1) 2) Import the data Select Contingency table from Chi-Square in MegaStat option from Add-Ins menu 3) 4) Select Chi-Square and Expected frequencies in Output options. Click Ok The expected values table Excel output is

Chi-square Contingency Table Test for Independence Pre-retirement Post-retirement 247 224.7418 75 Total 172 194.2582 419 Night 4-7 Observed Expected Observed 419.0000 Night 8-13 137 62 Expected Observed 73.4836 63.5164 137.0000 91 Night 14-21 40 51 Expected Night 22 or more Observed Expected Observed Expected 48.8103 42.1897 91.0000 54 54.0000 701 14 40 28.9643 25.0357 Total 376 325 376.0000 325.0000 701.0000 24.9281 chi-square 3 df 1.60E-05 p-value To test the hypothesis is that the length of stay is dependent of retirement at 1% significance level

The null and alternative hypothesis is, The null hypothesis is that the length of stay is independent ofretirement The alternative hypothesis is that the length of stay is dependent of retirement. a) The chi-square statistics is, From the Excel output, the chi-square test statistic is 24.9281 b) The degree of freedom is d.f.-(r-1)x (c-1) (4-1)x (2-) - 3

The chi-square critical value is, From the critical value table, the degrees of freedom which is 3 and the significance level 0.01, so chi-square critical values is 11.345 www.w The chi-square critical value is 11.345 c) The p-value is, From the Excel output, the p-value is 0.0000. The p-value is 0.0000 Decision The conclusion is that the significant p-value is less than 0.01 which is 0.0000, so the null hypothesis is rejected at 1% level of significance. There is sufficient evidence to indicate that the length of stay is dependent of retirement. The result is statistically significant