Adecco Workplace Insights Survey sampled men and women workers and asked if they

Question

Adecco Workplace Insights Survey sampled men and women workers and asked if they expected to get a raise or promotion this year (USA Today, February 16, 2012). Suppose the survey sampled 200 men and 200 women. If 104 of the men replied yes and 74 of the women replied yes, are the results statistically significant in that you can conelude a greater proportion of men are expecting to get a raise or a promotion this year? a. State the hypothesis test in terms of the population proportion of men and the population proportion of women? b. What is the sample proportion for men? Round your answer to two decimal places. What is the sample proportion for women? Round your answer to two decimal places. c. Use a .01 level of significance. What is the p-value? Round your answer to four decimal places. What is your conclusion?

Explanation / Answer

Test For Significance of Difference Of Proportion
Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate Hypothesis, There Is Significance between them H1: p1 > p2
Test Statistic
Sample 1 : X1 =104, n1 =200, P1= X1/n1=0.52
Sample 2 : X2 =74, n2 =200, P2= X2/n2=0.37
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.445
Q^ Value For Proportion= 1-P^=0.555
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.52-0.37)/Sqrt((0.445*0.555(1/200+1/200))
Zo =3.018
| Zo | =3.018
Critical Value
The Value of |Z | at LOS 0.01% is 2.326
We got |Zo| =3.018 & | Z | =2.326
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value: Right Tail -Ha : ( P > 3.0183 ) = 0.00127
Hence Value of P0.01 > 0.00127,Here we Reject Ho

a greater proportion of men are expecting to
get a raise or a promotion this year

ANSWERS

a,

p1 - p2 =0

p1-p2>0

b.

P1= X1/n1=0.52,

P2= X2/n2=0.37

c.( P > 3.0183 ) = 0.00127

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