Question

Research is conducted regarding the average age at retirement for three career groups. To test whether there is a relationship between ag of retirement and career in these groups, 482 employees, recently retired, are randomly selected. The resulting data are displayed below. C Age at retirement 56-60 61-65 Over 65 Total Attorney 40 30 75 80 63 College Professor 40 60 49 155 170 Secretary - 157 Total 218 149 482 At the 5% significance level, do the data provide sufficient evidence to conclude that an association exists between age of retirement and career? In this sample, if no association exists, how many college professors aged 61 - 65 would you expect to retire? Round to the nearest hundredths. In this sample, if no association exists, how many attorneys aged 56-60 would you expect to retire? Round to the nearest hundredths. The test statistic comes out to X2 = 8.2528. Choose the correct estimate of the p-value. Based on your p-value estimate, you will (not reject, reject) the null hypothesis.

Answer 1

Ans:

Expected number of college professors aged 61-65 to retire=218*170/482=76.89$\approx 77$

Expected number of attorneys aged 56-60 to retire=115*155/482=36.98$\approx 37$

Test statistic:

Chi square=8.2528

df=(3-1)*(3-1)=4

p-value=CHIDIST(8.2528,4)=0.0827

As,p-value>0.05,we fail to reject the null hypothesis.

we will not reject the null hypothesis.