Question

please show the work

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 697 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	241	175	416
8-13	78	72	150
14-21	30	60	90
22 or more	11	30	41
total	360	337	697

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=0.01.

(a) Find test value χ2=

(b) Find the d.f.:

(c) Find the critical value:

(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

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

Number of Nights	Pre-retirement	Post-retirement	Total
4-7	214.864	201.136	416
8-13	77.475	72.525	150
14-21	46.485	43.515	90
22 or more	21.176	19.824	41
Total	360	337	697

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
241	214.864	3.179176111
78	77.475	0.003557599
30	46.485	5.846084221
11	21.176	4.890015867
175	201.136	3.396162278
72	72.525	0.003800414
60	43.515	6.245093071
30	19.824	5.223515738
Total		28.7874053

(a)

So test statistics is:

(b)

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (4-1)*(2-1)=3

(c)

The critical value is : 7.815

(D)

Since so we reject the null hypothesis.

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.