A test is made of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$ $\bar { x } = 66$ The population standard deviation is $\sigma = 22$ Compute the value of the test statistic z and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.01 \text { level. }$
A) $0.27 , H _ { 0 } \text { rejected }$
B) $2.38 , H _ { 0 } \text { rejected }$
C) $0.27 , H _ { 0 } \text { not rejected }$
D) $2.38 , H _ { 0 } \text { not rejected }$

Question

A test is made of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$ $\bar { x } = 66$ The population standard deviation is $\sigma = 22$ Compute the value of the test statistic  z  and determine if $H _ { 0 }$ is rejected at the $\alpha = 0.01 \text { level. }$
A) $0.27 , H _ { 0 } \text { rejected }$
B) $2.38 , H _ { 0 } \text { rejected }$
C) $0.27 , H _ { 0 } \text { not rejected }$
D) $2.38 , H _ { 0 } \text { not rejected }$

Quizplus · Accepted Answer

The test statistic $z$ is calculated using the formula $z = \frac{\bar{x} - \mu}{\sigma / \sqrt{n}}$. Without the sample size $n$, we cannot compute $z$ directly from the information given. However, assuming a typical approach, choice D suggests a z-value that could be plausible for a significant difference if $n$ were known and the calculation followed standard procedures. The decision to reject $H_0$ depends on the comparison of the calculated z-value with critical z-values from the standard normal distribution at the $\alpha = 0.01$ level. For a two-tailed test at $\alpha = 0.01$, the critical z-values are approximately $\pm2.58$. Since $2.38$ is less than $2.58$, $H_0$ would not be rejected based on this level of significance.

A Test Is Made Of H0:μ=60 versus H1:μ≠60H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60H0​:μ=60 versus H1​:μ=60

A Test Is Made Of $H _ { 0 } : \mu = 60 \text { versus } H _ { 1 } : \mu \neq 60$