A 95% confidence interval infers that the population mean is
A) between 0 and 100%.
B) within $\pm$ 1.96 standard deviations of the sample mean.
C) within $\pm$ 1.96 standard errors of the sample mean.
D) within $\pm$ 1.645 standard deviations of the sample mean.
E) too large.

Question

A 95% confidence interval infers that the population mean is
A) between 0 and 100%.
B) within  $\pm$ 1.96 standard deviations of the sample mean.
C) within $\pm$ 1.96 standard errors of the sample mean.
D) within $\pm$ 1.645 standard deviations of the sample mean.
E) too large.

Quizplus · Accepted Answer

A 95% confidence interval implies that we are 95% confident that the true population mean falls within the range calculated from the sample data. The range is calculated as the sample mean plus or minus a margin of error, which is based on the standard error of the mean (SEM) rather than the standard deviation (SD) when the population SD is unknown. A 95% confidence interval using the SEM is calculated as follows: mean ± 1.96(SEM). Therefore, the answer is C.

A 95% Confidence Interval Infers That the Population Mean Is ±\pm±

A 95% Confidence Interval Infers That the Population Mean Is $\pm$