Question

A study is to be made to estimate the proportion of residents of a certain city and its suburbs who favor the construction of a nuclear power plant near the city. How large a sample is needed if one wishes to be at least 90% confident that the estimate is within 0.07 of the true proportion of residents who favor the construction of the nuclear power plant? Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. The sample should be people. (Round up to the nearest whole number.)

Answer 1

Solution,

Given that,

$\hat p$ =  1 - $\hat p$ = 0.5

margin of error = E = 0.07

At 90% confidence level

$\alpha$ = 1 - 90%

$\alpha$ = 1 - 0.90 =0.10

$\alpha$/2 = 0.05

Z$\alpha$/2 = Z_0.05 = 1.645

sample size = n = (Z_{$\alpha$ / 2} / E )² * $\hat p$ * (1 - $\hat p$ )

= (1.645 / 0.07)² * 0.5 * 0.5

= 138.06

sample size = n = 139