Question

It has been suggusted that the highest priority of retirees is travel. Thus, a study was...

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.

Homework Answers

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.

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