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 700 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 4−7 238 172 410 8−13 84 62 146 14−21 33 58 91 22 or more 17 36 53 Total 372 328 700 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=0.05. (a) χ2= (b) Find the degrees of freedom: (c) Find the critical value: (d) The final conclusion is A. 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. B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

Answer 1

a)

Applying chi square test:

Expected	Ei=row total*column total/grand total	Pre	Post	Total
	4-7	217.886	192.114	410
	8-13	77.589	68.411	146
	14-21	48.360	42.640	91
	22 or more	28.166	24.834	53
	total	372	328	700
chi square    χ2	=(Oi-Ei)2/Ei	Pre	Post	Total
	4-7	1.857	2.106	3.963
	8-13	0.530	0.601	1.131
	14-21	4.879	5.533	10.412
	22 or more	4.426	5.020	9.447
	total	11.692	13.260	24.952

χ2= 24.952

b)

degree of freedom(df) =(rows-1)*(columns-1)=

3

c)

for 3 df and 0.05 level of signifcance critical value       χ2=

7.815

d)

A. 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.