It has been suggusted that the highest priority of retirees is travel. Thus, a s

Question

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 687 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below.

With this information, construct a table of expected numbers.

The chi-squared value is 2= 32.6489368670556

Using =0.05, consider a test of H0: length of stay and retirement are not related vs. HA: length of stay and retirement are related. Note that this problem involves a 4×2 contingency table and that the magic number for evaluating such a table at the =0.05 level of significance is magic number = 7.81.

The final conclusion is

A. Accept H0. There is not sufficient evidence to conclude that the length of stay is related to retirement.
B. Reject H0. There is sufficient evidence to conclude that the length of stay is related to retirement.

Number of Nights Pre-retirement Post-retirement Total 47 242 161 403 813 78 66 144 1421 36 56 92 22 or more 11 37 48 Total 367 320 687

Explanation / Answer

Ans:

Test statistic:

chi square score=32.649

number of rows=2

number of columns=3

degree of freedom=(4-1)*(2-1)=3

p-value=CHIDIST(32.649,3)=0

critical chi square value=7.81

As,p-value<0.05,we reject null hypothesis.

Reject H0. There is sufficient evidence to conclude that the length of stay is related to retirement.

Option B is correct.

Observed(O) Number of Nights Pre-retirement Post-retirement Total 47 242 161 403 813 78 66 144 1421 36 56 92 22 or more 11 37 48 Total 367 320 687 Expected€ Number of Nights Pre-retirement Post-retirement Total 47 215.29 187.71 403 813 76.93 67.07 144 1421 49.15 42.85 92 22 or more 25.64 22.36 48 Total 367 320 687 (O-E)^2/E Number of Nights Pre-retirement Post-retirement Total 47 3.315 3.802 7.117 813 0.015 0.017 0.032 1421 3.517 4.033 7.550 22 or more 8.361 9.589 17.949 Total 15.208 17.441 32.649

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