Question: The Reynold Association surveyed retired senior executives who had returned to work. They found that after returning to work, 38% were employed by another organization, 32% were self-employed, 23% were either freelancing or consulting, and 7% had formed their own companies. To see if these percentages are consistent with those of Allegheny County residents, a local researcher surveyed 300 retired executives who had returned to work and found that 122 were working for another company, 85 were self employed, 76 were either freelancing or consulting, and 17 had formed their own companies. At the .10 significance level, test the claim that the percentages are the same for those people in Allegheny County.

Ho: The retired executives who returned to work are distributed as follows, 38% are employed by another organization, 32% are self-employed, 23% are either freelancing or consulting, and 7% have formed their own companies (claim).

Ha: The distribution is not the same as stated in the null hypothesis.

Complete the Chi-square Table

Sr Retirees Who Returned to Work Frequency of Observed (O) Frequency of Expected (E) (O-E)2/E Chi-square

Working for Another Co. 122

Self-employed 85

Free-lancing 76

Formed their own co. 17

Total 300 300

a. State the decision rule using the .01 significance level. (Make a statement such as: Reject Ho if > the critical value. You must indicate the specific critical value for this problem.)

b. What is the value of chi-square?

c. What is your decision regarding Ho? (Reject or Do Not Reject Ho?)