It is desired to test H0: μ = 55 against Ha: μ

Question

It is desired to test H0: μ = 55 against Ha: μ < 55 using α = .10. The population in question is uniformly distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If μ is really equal to 50, what is the power of this test?
A) .8531
B) .1469
C) .2938
D) .3531

Quizplus · Accepted Answer

The power of a test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. Here, we calculate the power by finding the probability that the test statistic falls in the critical region when μ = 50. The critical value for a one-tailed test at α = 0.10 is found using the standard normal distribution. The test statistic is calculated using the sample mean, standard deviation, and sample size. The power is then 1 minus the probability of a Type II error (failing to reject H0 when Ha is true), which is 0.1469, so the power is 0.8531.

It Is Desired to Test H0: μ = 55 Against