Question

In a sample of 410 adults, 246 had children. Construct a 90% confidence interval for the true population proportion of adults with children.

Give your answers as decimals, to three places

_______ < p < _______

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 246 / 410 = 0.600

1 - = 1 - 0.600 = 0.4

Z/2 = 1.645

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

= 1.645 * (((0.600 * 0.4) / 410)

Margin of error = E = 0.040

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.600 - 0.040 < p < 0.600 + 0.040

0.560 < p < 0.640