A test is made of $H _ { 0 } : \mu = 60$ versus $H _ { 1 } : \mu 60$. A sample of size $n = 77$ is drawn, and $\bar { x } = 64$. The population standard deviation is $\sigma = 23$. Compute the value of the test statistic $z$ and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.05$ level.
A) $1.53 , H _ { 0 }$ not rejected
B) $0.17 , H _ { 0 }$ not rejected
C) $1.53 , H _ { 0 }$ rejected
D) $0.17 , H _ { 0 }$ rejected

Question

A test is made of $H _ { 0 } : \mu = 60$ versus $H _ { 1 } : \mu > 60$. A sample of size $n = 77$ is drawn, and $\bar { x } = 64$. The population standard deviation is $\sigma = 23$. Compute the value of the test statistic $z$ and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.05$ level.
A) $1.53 , H _ { 0 }$ not rejected
B) $0.17 , H _ { 0 }$ not rejected
C) $1.53 , H _ { 0 }$ rejected
D) $0.17 , H _ { 0 }$ rejected

Quizplus · Accepted Answer

The test statistic $z$ is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$, where $\bar{x} = 64$, $\mu = 60$, $\sigma = 23$, and $n = 77$. Plugging in these values gives $z = \frac{64 - 60}{23 / \sqrt{77}} \approx 1.53$. At the $\alpha = 0.05$ level, the critical value for a one-tailed test is approximately 1.645. Since 1.53 is less than 1.645, $H_0$ is not rejected.

A Test Is Made Of H0:μ=60H _ { 0 } : \mu = 60H0​:μ=60

A Test Is Made Of $H _ { 0 } : \mu = 60$