Question

a graduate student wanted to estimate the average time spent studying among graduate students at her school. she randomly sampled graduate students from her school and obtained a 99% confidence interval of (17,25) hours/week. which of the following would be true if the level of confidence was lowered to 95%?

choose the correct answer below.

○ a. the width of the confidence interval would be smaller.
○ b. the width of the confidence interval would be larger.
○ c. the width of the confidence interval would remain the same.
○ d. more information is needed to determine what would happen to the width of the confidence interval

Explanation:

The width of a confidence interval is related to the confidence level. A higher confidence level requires a larger margin of error (because we want to be more sure that the interval contains the true population parameter), which makes the interval wider. Conversely, a lower confidence level requires a smaller margin of error, so the interval will be narrower.

Answer:

A. The width of the confidence interval would be smaller.