Find the standardized test statistic t for a sample with $$\mathrm { n } = 20 , \overline { \mathrm { x } } = 13.3 , \mathrm {~s} = 2.0 , \text { and } \alpha = 0.05 \text { if } \mathrm { H } _ { 1 } : \mu

Question

Find the standardized test statistic t for a sample with $$\mathrm { n } = 20 , \overline { \mathrm { x } } = 13.3 , \mathrm {~s} = 2.0 , \text { and } \alpha = 0.05 \text { if } \mathrm { H } _ { 1 } : \mu < 13.7$$ Round your answer to three decimal places.
A) -0.894
B) -0.872
C) -1.265
D) -1.233

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, $\overline{x} = 13.3$, $s = 2.0$, $n = 20$, and $\mu = 13.7$ (implied by $H_1: \mu < 13.7$). Plugging these values into the formula gives $ t = \frac{13.3 - 13.7}{(2.0 / \sqrt{20})} = -0.894 $ when rounded to three decimal places.

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