Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.

A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature. Construct the 95% confidence interval for the true proportion of all voters in the state who favor approval.

Answer 1

Solution :

Given that,

n = 865

x = 408

= x / n = 408 / 865 = 0.47

1 - = 1 - 0.47 = 0.53

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z _{/ 2} * [( * (1 - ) / n]

= 1.96 * ([(0.47 * 0.53) / 865]

= 0.0333

A 95% confidence interval for population proportion p is ,

- E < P < + E

0.47 - 0.0333 < p < 0.47 + 0.0333

0.4367 < p < 0.5033

(0.4367, 0.5033)