Question

Working at home: According to the U.S Census Bureau, 42% of men who worked at home were college graduates. In a sample of 514 women who worked at home, 158 were college graduates.

(c) Based on the confidence interval, is it reasonable to believe that the proportion of college graduates among women who work at home is the same as the proportion of college graduates among men who work at home? Explain.

yes/no, because 0.42 is/ is not contained in the confidence interval.

Answer 1

here confidence level is not given:

for 95% CI:

sample success x =		158
sample size          n=		514
sample proportion p̂ =x/n=		0.3074
std error se= √(p*(1-p)/n) =		0.0204
for 95 % CI value of z=		1.960
margin of error E=z*std error   =		0.0399
lower bound=p̂ -E                       =		0.2675
Upper bound=p̂ +E                     =		0.3473
from above 95% confidence interval for population proportion =(0.268,0.347)

c)since 0.42 is not contained in the Confidence interval:

No, because 0.42 is not contained in the confidence interval.