Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \overline { \mathrm { x } } = 6.9 , \mathrm {~s} = 2.0 \text {, and } \alpha = 0.05 \text { if } \mathrm { H } _ { \mathrm { a } } : \mu

Question

Find the standardized test statistic t for a sample with $\mathrm { n } = 20 , \overline { \mathrm { x } } = 6.9 , \mathrm {~s} = 2.0 \text {, and } \alpha = 0.05 \text { if } \mathrm { H } _ { \mathrm { a } } : \mu < 7.3 \text {. Round }$ your answer to three decimal places.
A)-0.894
B)-0.872
C)-1.265
D)-1.233

Quizplus · Accepted Answer

The correct answer is A.The standardized test statistic t is calculated as:$$t = \frac{\overline{x} - \mu_0}{s/\sqrt{n}}$$where $\overline{x}$ is the sample mean, $\mu_0$ is the hypothesized population mean, s is the sample standard deviation, and n is the sample size.In this case, we have $\mathrm { n } = 20 , \overline { \mathrm { x } } = 6.9 , \mathrm {~s} = 2.0 \text {, and } \alpha = 0.05 \text { if } \mathrm { H } _ { \mathrm { a } } : \mu < 7.3 $.Substituting these values into the formula, we get:$$t = \frac{6.9 - 7.3}{2.0/\sqrt{20}} = -0.894$$Therefore, the standardized test statistic t is -0.894, which is rounded to three decimal places.

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