Question

Working at home: According to the U.S Census Bureau, 34% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 170 were college graduates.

(a) Find a point estimate for the proportion of college graduates among women who work at home. Round the answer to at least three decimal places.

=0.340

(b) Construct a 90% confidence interval for the proportion of women who work at home who are college graduates. Round the answer to at least three decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 170 / 500 = 0.340

1 - = 0.660

Z/2 = 1.645

Margin of error = E = Z / 2 * (( * (1 - )) / n)

= 1.645 * [(0.340 * 0.660) / 500]

= 0.035

At 90% confidence interval for population proportion p is ,

- E < p < + E

0.340 - 0.035 < p < 0.340 + 0.035

0.305 < p < 0.375

Lower bound = 0.305

Upper bound = 0.375