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 conclude 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.

Given that 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).

Men Women Total

Surveyed n 200 200 400

Yes replied 104 74 178

Proportion 0.52 0.37 0.445

Pooled proportion = 0.445

[tex]H_0: p_1=p_2\\H_a: p_1>p_2[/tex]

(Right tailed test at 5% level)

p difference = 0.15

std error =

z is 3.0183.

The value of p is .00126.

[tex]\sqrt{0.445(0.555)/{1/200+1/200} } \\=0.0496[/tex]

The result is significant at p < .05

We can conclude that a greater proportion of men are expecting to get a raise or a promotion this year