Question

A university surveyed recent graduates of the English department about their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000. Assume for purposes of this problem that the population standard deviation is known, and it is $2,500. A 95% confidence interval is constructed. What does the confidence interval mean?

Group of answer choices

There is a 95% probability that the population parameter will not lie within the interval constructed using the sample's data.

The population mean is not in the interval.

The population mean is in the interval.

There is a 95% probability that the population parameter will lie within the interval constructed using the sample's data.

Answer 1

Solution:

Correct option is

There is a 95% probability that the population parameter will lie within the interval constructed using the sample's data.

Explanation:

The meaning of 95% confidence interval : 95% confidence interval means that there is 95% probability that the true population parameter will lie in the interval we constructed .

If we draw several samples of size n and we constructed the 95% confidence intervals using these samples , then 95% of these intervals will contain the true population parameter.