Question

1. In order to estimate the proportion of residents in a town that are female you take a sample of size 100. The sample proportion is 0.53.
   1. If the town has 20,000 residents, what is your best guess for the number of female residents?
   2. Compute a 95% confidence interval for the proportion of residents in the town that are female.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.53

1 - = 1 - 0.53 = 0.47

Z/2 = 1.96

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

= 1.96 * (((0.53 * 0.47) / 100)

Margin of error = E = 0.098

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.53 - 0.098 < p < 0.53 + 0.098

0.432 < p < 0.628

The 95% confidence interval for the population proportion p is : 0.432 , 0.628