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 690690 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below.Number of NightsPre-retirementPost-retirementTotal4−72461624088−13766714314−2137508722 or more193352Total378312690With this information, construct a table of estimated expected values.Number of NightsPre-retirementPost-retirement4−7 8−13 14−21 22 or more Now, with that information, determine whether the length of stay is independent of retirement using α=0.05.(a) χ2= (b) Find the degrees of freedom= (d) The final conclusion is:A. 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.B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

Name: It has been suggusted that the highest priority of retirees is travel.
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Description: 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 690690 travelers were asked how long they stayed

Null hypothesis: H0: The length of stay is independent of retirement. Alternative hypothesis: H1: The length of stay is not independent of retirement. Observed values with marginal totals: The chi-square test for independents is appropriate in this situation.Expected values: Expected values are the product of the column and row total divided by the table total.a) The test statistic is calculated as follows: χ2=∑O-E2E =246-223.51302223.5130+…+33-23.5130223.5130 =17.4186 The test statistic is 17.4186. b) The degrees of freedom is (r-1)(c-1)=(4-1)(2-1)=3. c) The p-value is 0.00058 using the Excel formula “=CHISQ.DIST.RT(17.4186,3)” Decision: The p-value is 0.00058. Assume the level of significance is 0.05. The p-value is less than level of significance. Since p-value<α, reject null hypothesis. 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.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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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 690690 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	246	162	408
8−13	76	67	143
14−21	37	50	87
22 or more	19	33	52
Total	378	312	690

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 α=0.05.

(a) χ2=

(b) Find the degrees of freedom=

(d) The final conclusion is:
A. 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.
B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

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