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

Answer: 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.

Step-by-step explanation:

Interpretation for 95% confidence interval :

A person can be 95% confident that the true population parameter lies in it.

By considering the given information , we have

population parameter→ p (Proportion of people who think climate change )

95 percent confidence interval = (0.146, 0.214)

Interpretation : We can be 95% confident that the true population proportion of people who think climate change lies between 0.146 and 0.214.

So , the correct answer is

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.