We have calculated a confidence interval based on a sample of size n = 100. After looking over our work, we realized that the sample size was actually 400. How will the corrected interval compare to the original interval?
A) The corrected interval will be the same width.
B) The corrected interval will be one-fourth as wide.
C) The corrected interval will be four times as wide.
D) The corrected interval will be one-half as wide.
E) The corrected interval will be twice as wide.

Question

Quizplus · Accepted Answer

The width of a confidence interval is inversely proportional to the square root of the sample size. Therefore, when the sample size increases by a factor of 4 (from n=100 to n=400), the width of the interval will be divided by 2. So, the corrected interval will be one-half as wide as the original interval.

We Have Calculated a Confidence Interval Based on a Sample