Which of the following is the test statistic for a one-sample test for mean when the population standard deviation is unknown?
A)$t=\frac{\bar{x}-\mu 0}{s / \sqrt{n}}$

B)$z=\frac{s / \sqrt{n}}{\bar{x}-\mu_{0}}$

C)$z=\frac{\bar{x}-\mu_{0}}{\sigma / \sqrt{n}}$

D)$t=\frac{\sigma / \sqrt{n}}{\bar{x}-\mu 0}$

Question

Which of the following is the test statistic for a one-sample test for mean when the population standard deviation is unknown?
A)$t=\frac{\bar{x}-\mu 0}{s / \sqrt{n}}$

B)$z=\frac{s / \sqrt{n}}{\bar{x}-\mu_{0}}$

C)$z=\frac{\bar{x}-\mu_{0}}{\sigma / \sqrt{n}}$

D)$t=\frac{\sigma / \sqrt{n}}{\bar{x}-\mu 0}$

Quizplus · Accepted Answer

When the population standard deviation is unknown, we use the t-distribution and the test statistic is given by t = (x̄ - μ) / (s / sqrt(n)), where x̄ is the sample mean, μ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size. Option A matches this formula. The other options either use the z-distribution (which is only applicable when the population standard deviation is known or the sample size is very large) or use incorrect formulas.

Which of the Following Is the Test Statistic for a One-Sample