Question

A committee studying employer-employee relations proposed that each employee would rate his or her immediate supervisor and in turn the supervisor would rate each employee. To find reactions regarding the proposal, 120 office personnel and 180 plant personnel were selected at random. Sixty-eight percent of the office personnel and 140 of the plant personnel were in favor of the proposal. a. Using a .025 level of significance, test the hypothesis that the proportion in favor is higher for plant personnel (show all steps).

Answer 1

Given:

n1=120, n2=180, = 68%=0.68, X2 = 140, $\alpha$ = 0.025

Hypothesis:

Ho: P1 = P2

Ha: P1 < P2 (The proportion in favor is higher for plant personnel)

Where,

P1 = proportion of office personnel

P2 = proportion of plant personnel

Calculation:

$\hat{p1}$ = 68%=0.68

X1 = n1*$\hat{p1}$ = 120*0.68 = 81.6

12140 p2 =-=-= 0.78 n2 180

X1X281.6140 nln2 120180 0.74

Q = 1-P= 1-0.74 = 0.26

Test statistic:

pl - p2 0.68-0.78 120180

Critical value:

Z_$\alpha$ = Z_0.025 = -1.96

Conclusion:

Test statistic > Critical value, i.e -1.89 > -1.96, That is Fail to raject Ho at 2.5% level of significance.

Therefore, there is No difference between the proportion of office personnel & plant personnel.