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.
-$$\mathrm { H } _ { \mathrm { a } } : \mu 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6$$
A) $z = 3.29$; not supported
B) $z = 6.25$; supported
C) $z = 2.06$; supported
D) $z = 2.06$; not supported

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.
-$$\mathrm { H } _ { \mathrm { a } } : \mu > 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6$$
A) $z = 3.29$; not supported
B) $z = 6.25$; supported
C) $z = 2.06$; supported
D) $z = 2.06$; not 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, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values, $z = \frac{51 - 50}{3.6 / \sqrt{55}} \approx 2.06$. At a 0.05 significance level, the critical z-value for a one-tailed test is approximately 1.645. Since 2.06 > 1.645, the result is statistically significant, and the alternative hypothesis ($\mu > 50$) is supported.

Find the Value of the Standard Score, Z, and Determine Ha:μ>50,n=55,x‾=51,σ=3.6\mathrm { H } _ { \mathrm { a } } : \mu > 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6Ha​:μ>50,n=55,x=51,σ=3.6

Find the Value of the Standard Score, Z, and Determine $\mathrm { H } _ { \mathrm { a } } : \mu > 50 , \mathrm { n } = 55 , \overline { \mathrm { x } } = 51 , \sigma = 3.6$