It is desired to test $\mathrm { H } _ { 0 } : \mu = 40$ against $\mathrm { H } _ { 1 } : \mu

Question

It is desired to test $\mathrm { H } _ { 0 } : \mu = 40$ against $\mathrm { H } _ { 1 } : \mu < 40$ using $\alpha = 0.10$. The population in question is uniformly distributed with a standard deviation of 10 . A random sample of 36 will be drawn from this population. If $\mu$ is really equal to 35 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?
A) 0.0427
B) 0.9573
C) 0.4573
D) 0.0854

Quizplus · Accepted Answer

The correct answer is A.The probability of a Type II error is the probability of failing to reject the null hypothesis when it is false. In this case, the null hypothesis is that the mean is 40, and the alternative hypothesis is that the mean is less than 40. The population standard deviation is 10, and a random sample of 36 will be drawn from this population. If the mean is really equal to 35, then the probability of a Type II error is 0.0427.

It Is Desired to Test H0:μ=40\mathrm { H } _ { 0 } : \mu = 40H0​:μ=40

It Is Desired to Test $\mathrm { H } _ { 0 } : \mu = 40$