Find the value of the standard score, z, and determine whether the alternative hypothesis is supported or not supported at a 0.05 significance level.
-$\mathrm { H } _ { \mathrm { a } } : \mu \neq 18.7 , \mathrm { n } = 11 , \overline { \mathrm { x } } = 20.5 , \sigma = 7$
A) $z = - 0.85$; supported
B) $z = - 0.85$; not supported
C) $\mathrm { z } = 0.85$; supported
D) $z = 0.85$; not supported

Question

Quizplus · Accepted Answer

The standard score (z) is calculated using the formula $z = \frac{\overline{x} - \mu}{\sigma / \sqrt{n}}$, where $\overline{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values, $z = \frac{20.5 - 18.7}{7 / \sqrt{11}} \approx 0.85$. At a 0.05 significance level for a two-tailed test, the critical z-values are approximately $\pm1.96$. Since 0.85 does not exceed these critical values, the alternative hypothesis ($\mathrm{H}_a: \mu \neq 18.7$) is not supported.

Find the Value of the Standard Score, Z, and Determine Ha:μ≠18.7,n=11,x‾=20.5,σ=7\mathrm { H } _ { \mathrm { a } } : \mu \neq 18.7 , \mathrm { n } = 11 , \overline { \mathrm { x } } = 20.5 , \sigma = 7Ha​:μ=18.7,n=11,x=20.5,σ=7

Find the Value of the Standard Score, Z, and Determine $\mathrm { H } _ { \mathrm { a } } : \mu \neq 18.7 , \mathrm { n } = 11 , \overline { \mathrm { x } } = 20.5 , \sigma = 7$