Question

A survey was done among retired senior executives who had returned to work. It found that after returning to work, 36% were employed by another organization, 31% were self-employed, 26% were either freelancing or consulting, and 7% had formed their own company. To see if these percentages are consistent with residents of a county, a local researcher surveyed 300 retired executives who have returned to work and found that 102 were working for another company, 87 were self-employed, 96 were either freelancing or consulting, and 15 have formed their own companies. At = 0.1, test the claim that the percentages are the same for those people in that county. Is there enough evidence to reject the claim?

Answer 1

Ho : The percentages are the same for those people in that county.

Ha : The percentages are not same for those people in that county.

Given that :

N=300

Test statistic formula is ,

O: observed values

E: expected values

Degrees of freedom = k - 1

k is the number of categories

k=4

DF= 4-1 = 3

To get the P value using Excel function,

P value = 0.086

Decision rule :

We reject Ho , if P value is less than the significance level ().

As p value ( 0.086 ) is less than the significance level (0.10) , so we reject Ho.

Conclusion :

There is enough evidence to reject the claim that the percentages are the same for those people in that county.