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

# of nights	pre-retirement	post-retirement	total
4-7	239	169	408
8-13	78	68	146
14-21	34	58	92
22 or more	13	37	50
Total	364	332	696

With this information, construct a table of estimated expected values.

# 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 alpha = 0.01

a) chi squared =

b) Find the degrees of freedom:

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

(a)

Estimated Expected Value is given by:

# nights	pre - retirement	post - retirement	Total
4 - 7	364X408/696=213.38	194.62	408
8 - 13	76.36	69.64	146
14 -21	48.11	43.89	92
22 or more	26.15	23.85	50
Total	364	332	696

Test statistic is got as follows:

Observed (O)	Expected (E)	(O - E)2/E
239	213.38	3.08
169	194.62	3.37
78	76.36	0.04
68	69.64	0.04
34	48.11	4.14
58	43.89	4.54
13	26.15	6.61
37	23.85	7.25
Total = =		29.07

So,

= 29.07

(b)

Degrees of freedom = (r - 1) X (c - 1)

                                 =( 4 - 1) X (2 - 1) = 3

(c)

= 0.01

From Table, critical value of = 11.3449

(d)

Correct option:

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.