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 672 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 4−7 231 161 392 8−13 76 67 143 14−21 36 53 89 22 or more 15 33 48 Total 358 314 672 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: (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) applying chi square tesst:

Expected	Ei=row total*column total/grand total	Pre	Post	Total
	4-7	208.83	183.17	392
	8-13	76.18	66.82	143
	14-21	47.41	41.59	89
	22 or more	25.57	22.43	48
	total	358	314	672
chi square    χ2	=(Oi-Ei)2/Ei	Pre	Post	Total
	4-7	2.353	2.683	5.035
	8-13	0.000	0.000	0.001
	14-21	2.748	3.133	5.880
	22 or more	4.370	4.983	9.353
	total	9.471	10.798	20.2696

X² =20.2696

b)

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

3

c)

critical value =11.345

d) 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.