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 675675 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	230	161	391
8−13	84	60	144
14−21	34	57	91
22 or more	13	36	49
Total	361	314	675

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 ?=0.05α=0.05.

(a) Find the test statistic: ?2=χ2=

(b) Find the degrees of freedom:  ??=df=

(c) Find the critical value: ?2=χ2=

(d) The final conclusion is

A. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.
B. 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.

Answer 1

The statistic software output for this problem is:

(a) Find the test statistic: ?2 = 29.6568

(b) Find the degrees of freedom:  ?? = 3

(c) Find the critical value: ?2 = 7.815

(d) Option B