Asurvey 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.

a) 0.435 < p < 0.508

b) 0.444 < p < 0.500

c) 0.471 < p < 0.472

d) 0.438 < p < 0.505

D) 0.438 < p < 0.505

Step-by-step explanation:

We know that the confidence interval for population proportion is given by :-

, where n= sample size

= Sample proportion.

z* = critical value.

Given : A survey of 865 voters in one state reveals that 408 favor approval of an issue before the legislature.

i.e. n= 865

Two-tailed critical avlue for 95% confidence interval : z* = 1.96

Then, the 95 % confidence interval for the true proportion of all voters in the state who favor approval will be :-

Thus, the required 95% confidence interval : (0.438, 0.505)

Hence, the correct answer is D) 0.438 < p < 0.505