Question

It has been suggested 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 683683 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	233	165	398
8-13	81	74	155
14−21	37	50	87
22 or more	12	31	43
Total	363	320	683

With this information, construct a table of expected numbers.

Number of Nights	Pre-retirement	Post-retirement
4−7
8−13
14-21
22 or more

The chi-squared value is ?2=χ2= 19.642779967698

Using ?=0.05α=0.05, consider a test of ?0:H0: length of stay and retirement are not related vs. ??:HA: length of stay and retirement are related. Note that this problem involves a 4×24×2 contingency table and that the magic number for evaluating such a table at the ?=0.05α=0.05 level of significance is magic number = 7.81.

The final conclusion is

A. Reject ?0.H0. There is sufficient evidence to conclude that the length of stay is related to retirement.
B. Accept ?0.H0. There is not sufficient evidence to conclude that the length of stay is related to retirement.

Note: You can earn partial credit on this problem.

Answer 1

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