The formula for a 100(1 - α)% confidence interval for the mean μ when the population standard deviation is unknown is ________.
A)$x_{i}-\bar{x} /(\sigma / \sqrt{n})$

B)$\bar{x} \pm t_{\alpha} / 2 n-1(s / \sqrt{n})$

C)$\bar{x} \pm_{z} \alpha / 2(\sigma / \sqrt{n})$

D)$-\frac{(\sigma / \sqrt{n})}{z \alpha / 2}$

Question

The formula for a 100(1 - α)% confidence interval for the mean μ when the population standard deviation is unknown is ________.
A)$x_{i}-\bar{x} /(\sigma / \sqrt{n})$

B)$\bar{x} \pm t_{\alpha} / 2 n-1(s / \sqrt{n})$

C)$\bar{x} \pm_{z} \alpha / 2(\sigma / \sqrt{n})$

D)$-\frac{(\sigma / \sqrt{n})}{z \alpha / 2}$

Quizplus · Accepted Answer

This is the formula for a confidence interval for the mean when the population standard deviation is unknown. The value of tα/2 represents the critical value from the t-distribution with n-1 degrees of freedom, which depends on the level of confidence and is used to determine the width of the interval. The formula uses the sample mean and sample standard deviation to estimate the population mean.

The Formula for a 100(1 - α)% Confidence Interval for the Mean