Question

A random sample of 1,175 people in a certain country were asked whether they thought climate change was a problem. The sample proportion of those who think climate change is a problem was calculated, and a 95 percent confidence interval was constructed as (0.146, 0.214). Which of the following is a correct interpretation of the interval?

a) We are 95 percent confident that any sample of 1,175 people will produce a sample proportion between 0.146 and 0.214.

B)We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.

C)We are 95 percent confident that the proportion of people in the sample who think climate change is a problem is between 0.146 and 0.214.

D)The probability that 95 percent of all people in the country who think climate change is a problem is between 0.146 and 0.214. E)The probability is 0.95 that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.

Answer 1

Solution:

Given:  A 95 percent confidence interval for proportion of those people who think climate change is a problem (0.146, 0.214).

We have to find the correct interpretation of the interval.

A confidence interval is an interval estimate about the population parameter that will lie within the limits of interval with specified confidence level.

Thus if interpretation contains sample statistic instead of population parameter then these interpretations are incorrect.

Also we do not use word probability for confidence level.

Thus correct answer is:

B) We are 95 percent confident that the proportion of all people in the country who think climate change is a problem is between 0.146 and 0.214.