Question

A poll reported that only 593 out of a total of 1594 adults in a particular region said they had a​ "great deal of​ confidence" or​ "quite a lot of​ confidence" in the public school system. This was down 5 percentage points from the previous year. Assume the conditions for using the CLT are met.

Interpret this interval. Select the correct choice below and fill in the answer boxes to complete your choice.

​(Type integers or decimals rounded to three decimal places as​ needed.)

A .There is a __ ​% chance that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between __ and __ .

B. We are __ ​% confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between __and __ .

C. We are __ ​% confident that the every sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between __ and __ .

D. There is a __​% chance that the sample proportion of adults having a great deal or quite a lot of confidence in the public schools is between __ and __ .

Answer 1

sample proportion, = 0.372
sample size, n = 1594
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.372 * (1 - 0.372)/1594) = 0.0121

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

Margin of Error, ME = zc * SE
ME = 1.96 * 0.0121
ME = 0.0237

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.372 - 1.96 * 0.0121 , 0.372 + 1.96 * 0.0121)
CI = (0.348 , 0.396)

B. We are 95% confident that the population proportion of adults having a great deal or quite a lot of confidence in the public schools is between 0.348 and 0.396