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

Question

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.
-$$\mathrm { H } _ { \mathrm { a } } : \mu < 10 , \mathrm { n } = 18 , \overline { \mathrm { x } } = 7.5 , \sigma = 1.7$$
A) $z = 7.5$; supported
B) $z = - 6.24$; supported
C) $z = - 6.24$; not supported
D) $z = 1.7 . ;$ supported

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 under the null hypothesis, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{7.5 - 10}{1.7 / \sqrt{18}} \approx -6.24$. Since the z-score is significantly less than 0 and we have a left-tailed test ($\mu < 10$), the result is statistically significant at the 0.05 level, supporting the alternative hypothesis.

Find the Value of the Standard Score, Z, and Determine Ha:μ<10,n=18,x‾=7.5,σ=1.7\mathrm { H } _ { \mathrm { a } } : \mu < 10 , \mathrm { n } = 18 , \overline { \mathrm { x } } = 7.5 , \sigma = 1.7Ha​:μ<10,n=18,x=7.5,σ=1.7

Find the Value of the Standard Score, Z, and Determine $\mathrm { H } _ { \mathrm { a } } : \mu < 10 , \mathrm { n } = 18 , \overline { \mathrm { x } } = 7.5 , \sigma = 1.7$