Find the standardized test statistic t for a sample with $$\mathrm { n } = 25 , \overline { \mathrm { x } } = 14 , \mathrm {~s} = 3 \text {, and } \alpha = 0.005 \text { if } \mathrm { H } _ { 1 } : \mu 13 \text {. Round }$$ your answer to three decimal places.
A) 1.667
B) 1.997
C) 1.452
D) 1.239

Question

Find the standardized test statistic t for a sample with $$\mathrm { n } = 25 , \overline { \mathrm { x } } = 14 , \mathrm {~s} = 3 \text {, and } \alpha = 0.005 \text { if } \mathrm { H } _ { 1 } : \mu > 13 \text {. Round }$$ your answer to three decimal places.
A) 1.667
B) 1.997
C) 1.452
D) 1.239

Quizplus · Accepted Answer

The standardized test statistic $ t $ is calculated using the formula $ t = \frac{\overline{x} - \mu}{s / \sqrt{n}} $, where $\overline{x}$ is the sample mean, $s$ is the sample standard deviation, $n$ is the sample size, and $\mu$ is the population mean under the null hypothesis. Here, $\overline{x} = 14$, $s = 3$, $n = 25$, and $\mu = 13$ (implied by $H_1: \mu > 13$). Plugging these values into the formula gives $ t = \frac{14 - 13}{3 / \sqrt{25}} = \frac{1}{3 / 5} = \frac{5}{3} = 1.667$.

Find the Standardized Test Statistic T for a Sample With \mathrm