Question

In a sample of 100 women, 30 percent had a college degree, while in a sample of 100 men, 25 percent had a college degree. (a) Find a 95 percent confidence interval for the population proportion of women having a college degree. (b) Find a 95 percent confidence interval for the population proportion of men having a college degree. (c) Find a 95 percent confidence interval for the difference in population proportions of women and men having college degrees.

Answer 1

Women:

n1 = 100

p1 = 30/100 = 0.3

At 95% CI, Z = 1.96

95% CI for proportions = p1 +* Z*sqrt(p1*(1-p1)/n1)

= 0.3 +- 1.96*sqrt(0.3*0.7/100)

= 0.3 +- 0.089

= (0.211, 0.389)

Men:

n2 = 100

p2 = 25/100 = 0.25

At 95% CI, Z = 1.96

95% CI for proportions = p2 +* Z*sqrt(p2*(1-p2)/n2)

= 0.25 +- 1.96*sqrt(0.25*0.75/100)

= 0.25 +- 0.085

= (0.165, 0.285)

Difference of Population Proportions:

95% CI for difference of proportions:

= (p1-p2) +- Z*sqrt( (p1*(1-p1)/n1 + p2*(1-p2)/n2)

= (0.3-0.25) +- 1.96*sqrt( 0.3*0.7/100 + 0.25*0.75/100)

= 0.05 +- 0.1235

= (-0.073 , 0.1735)

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