Question

7. A random sample of size n is collected from a considerably larger population

of size N. That sample is used to create a 95% confidence interval to estimate a
population proportion. Using the same sample proportion, the confidence
interval would be narrower if:
(A) A smaller sample size was used.
(B) A t-procedure was used instead of a z-procedure.
(C) A higher confidence level was used.
(D) The population size N was larger.
(E) A lower confidence level was used.​

Answer 1

B. Larger sample size and lower confidence level

Explanation:

The margin of error of a confidence interval is given by the following formula:

In which is the standard deviation of the population and n is the size of the sample.

z is related to the confidence level. The higher the confidence level, the higher the value of Z.

So, the margin of error is direct proportion to the confidence level and inverse proportional to the sample size.

We want to decrease the margin of error.

So the correct answer is:

B. Larger sample size and lower confidence level

Answer 2

(E) A lower confidence level was used.

Explanation:

The correct answer is (E). With the sample proportion remaining the same, a lower confidence level results in a lower margin of error and a narrower interval.