A survey first taken of 410 workers showed that 182 of them said that it was ser

Question

A survey first taken of 410 workers showed that 182 of them said that it was seriously unethical to monitor employee e-mail. Secondly, when 123 senior-level bosses were surveyed, 42 said that it was seriously unethical to monitor employee e-mail. a) Use a 0.05 significance level to test the claim that for those saying that monitoring e-mail is seriously unethical, the proportion of employees is greater than the proportion of bosses. Claim: p1 p2 Ho: p1 p2 H1: p1 p2 b) What is the rejection result? Do not reject the null hypothesis. Reject the null hypothesis. Not enough information. c) What is the conclusion? The sample data does not provide sufficient evidence to support the claim that the proportion of employees is greater than the proportion of bosses. The sample data provides evidence to support the claim that the proportion of employees is greater than the proportion of bosses. The sample data provides sufficient evidence to warrant rejection of the claim that the proportion of employees is greater than the proportion of bosses. The sample data does not provide sufficient evidence to warrant rejection of the claim that the proportion of employees is greater than the proportion of bosses.

Explanation / Answer

Null, There Is No Significance between them Ho: p1 = p2
Alternate, proportion of employees is greater than the proportion of bosses H1: p1 > p2
Test Statistic
Sample 1 : X1 =182, n1 =410, P1= X1/n1=0.444
Sample 2 : X2 =42, n2 =123, P2= X2/n2=0.341
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.42
Q^ Value For Proportion= 1-P^=0.58
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.444-0.341)/Sqrt((0.42*0.58(1/410+1/123))
Zo =2.019
| Zo | =2.019
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =2.019 & | Z | =1.645
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 2.0187 ) = 0.02176
Hence Value of P0.05 > 0.02176,Here we Reject Ho

[ANSWERS]
1. Ho: p1 = p2 , H1: p1 > p2
2. Reject Ho, when Ho> 1.645
3. Reject Ho
4. The sample data provides evidence to support the claim that the proportion of
employees is greater than the proportion of bosses

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