Which of the following statements is false?
A) The width of a confidence interval of the population mean narrows when the sample size increases.
B) The width of a confidence interval of the population mean narrows when the value of the sample mean increases.
C) The width of a confidence interval of the population mean widens when the confidence level increases.
D) The width of a confidence interval of the population mean is affected by the choice of confidence level.

Question

Quizplus · Accepted Answer

The width of a confidence interval of the population mean narrows when the sample size increases because a larger sample size leads to a smaller standard error. The width of a confidence interval of the population mean widens when the confidence level increases because a higher confidence level requires a wider interval to capture the population mean with greater certainty. The width of a confidence interval of the population mean is affected by the choice of confidence level, as mentioned in the explanation for choice C. However, the width of a confidence interval of the population mean does not narrow as the value of the sample mean increases; in fact, the opposite may occur, as a larger sample mean may lead to a larger standard error and a wider interval.

Which of the Following Statements Is False