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 691 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	235	175	410
8−13	84	63	147
14−21	31	59	90
22 or more	12	32	44
Total	362	329	691

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)  χ2=

(b) Find the degrees of freedom:

(c) Find the critical value:  

Answer 1

We have to find out Expected Frequencies:

Ei = (Corresponding row total * Corresponding column total) / sample size

For First cell:

E1 = (410 * 362) / 691 = 214.79

E2 = (410 * 329) / 691 = 195.21

Similarly solve for all other cells,

We have calculated for expected frequencies and presented in the following table:

Expected Frequencies:

Number of Nights	Pre -retirement	Post-retirement	Total
4 - 7	214.79	195.21	410.00
8 - 13	77.01	69.99	147.00
14 - 21	47.15	42.85	90.00
22 or more	23.05	20.95	44.00
Total	362.00	329.00	691.00

a)

Computational Table:

	Oi	Ei	(Oi-EI)	(Oi-Ei)2	(Oi-Ei)2/Ei
	235	214.79	20.21	408.4377	1.901566
	84	77.01	6.99	48.85828	0.63444
	31	47.15	-16.15	260.7921	5.531226
	12	23.05	-11.05	122.1169	5.297763
	175	195.21	-20.21	408.4377	2.092301
	63	69.99	-6.99	48.85828	0.698076
	59	42.85	16.15	260.7921	6.08603
	32	20.95	11.05	122.1169	5.82915
Total	691	691.00			28.07

Test statistic:

b)

Degrees of Freedom = (r-1) * (c-1)

Where, r = Number of rows = 4

c = Number of columns = 2

Degrees of Freedom = (r-1) * (c-1) = (4-1) * (2-1) = 3*1 = 3

C)

Critical value:

.........................From Chi square table

Conclusion:

Test statistic > Critical value, i.e. 28.07 > 11.34, That is Reject Ho at 1% level of significance.

Therefore, The length of stay is dependent of retirement