A survey of 865 voters in one state reveals that 408 favor approval of an issue....

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

A) 0.444 < p < 0.500

B) 0.471 < p < 0.472

C) 0.438 < p < 0.505

D) 0.435 < p < 0.508

Solutions

Expert Solution

Solution :

Given that,

n = 865

x = 408

Point estimate = sample proportion = = x / n = 0.472

1 - = 0.528

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} * $\sqrt$ (( * (1 - )) / n)

= 1.96 * ( $\sqrt$ ((0.472*0.528) / 865)

= 0.033

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.472 - 0.033 < p < 0.472 + 0.033

0.438 < p < 0.505

Option c is correct.

orchestra answered 1 year ago

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