It is desired to test $H _ { 0 } : \mu = 12$ against $H _ { \mathrm { a } } : \mu \neq 12$ using $\alpha = 0.05$. The population in question is uniformly distributed with a standard deviation of $2.0$. A random sample of 100 will be drawn from this population. If $\mu$ is really equal to $11.9$, what is the value of $\beta$ associated with this test?
A) .9209
B) .0395
C) .0791
D) .4210

Question

Quizplus · Accepted Answer

The power of the test is the probability of correctly rejecting the null hypothesis when the alternative is true. Here, $\beta$ is the probability of a Type II error, which is 1 minus the power. Given the sample size, standard deviation, and significance level, the power can be calculated, and $\beta$ is found to be approximately 0.9209.

It Is Desired to Test H0:μ=12H _ { 0 } : \mu = 12H0​:μ=12

It Is Desired to Test $H _ { 0 } : \mu = 12$