MS Module 4 Hypotheses and Test Procedures homework assignment

(The attached PDF file has better formatting.)

A population has a normal distribution with a mean μ0 of 61 and a standard deviation of 7.4

One group from this population has been treated to reduce its mean; we assume it is still normally distributed with the same standard deviation. A sample of size 23 from this treated group has a sample mean of and a true mean of μʹ.

●    The null hypothesis is H0: μʹ = μ0.
●    The one-sided alternative hypothesis is Ha: μʹ < μ0.

We reject the null hypothesis if ≤ 59.6

A.    What is the standard deviation of the sample mean?
B.    What is the z statistic value to test the null hypothesis?
C.    What is the probability of a Type I error for this one-sided (lower-tailed) test?
D.    If the true mean of the sample μʹ is 60.1, what is the probability of a Type II error for this test?

(To check your solutions, review the posting on practice exam questions for this module.)