Question

Suppose a 95% confidence interval for μ has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would ________. (Assume that the sample statistics gathered would not change very much for the new sample.) A) be larger than the current interval width. B) be narrower than the current interval width. C) be the same as the current interval width.D) be unknown until actual sample sizes and reliability levels were determined.

Answer 1

B) be narrower than the current interval width

Explanation:

Given that a 95% confidence interval for μ has been constructed.

This confidence interval would depend on the margin of error which in turn depends on the standard error and sample size.

Margin of error = Critical value *std dev/ sqrt of sample size n

Hence when sample size increases, n increases so square root of n increases, which in turn decreases the margin of error.

So confidence interval would become narrower.

B) be narrower than the current interval width