Question

20. Working at home: According to the U.S. Census Bureau, 43% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 162 were college graduates.

a. Find a point estimate for the proportion of college graduates among women who work at home.

b. Construct a 98% confidence interval for the proportion of women who work at home who are college graduates.

Answer 1

a) The point estimate for the proportion of college graduates among women who work at home is computed here as: p = x/n = 162/500 = 0.324

Therefore 0.324 is the required point estimate here.

b) From standard normal tables, we have:

P(Z < 2.326) = 0.99

Therefore,
P(- 2.326 < Z < 2.326) = 0.98

Now the confidence interval here is obtained as:

This is the required confidence interval here.