Question

A random sample of 100 observations from a population with standard deviation 23.35 yielded a sample mean of 94.5.

1. Given that the null hypothesis is μ=90, and the alternative hypothesis is μ>90 and using α=.05, find the following:
(a) Test statistic =
(b) P - value:
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

2. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ≠90 and using α=.05, find the following:
(a) Test statistic =
(b) P - value:

(c) The conclusion for this test (part 2) is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

Answer 1

1. a. As population standard deviation is known we will use z test statistics

b. P value is

c. As P value is less than alpha=0.05

We reject the null hypothesis

So correct answer is A. Reject the null hypothesis

2. a. As population standard deviation is known we will use z test statistics

b. P value is

c. As P value is greater than alpha=0.05, we fail to reject the null hypothesis

So correct answer is B. There is insufficient evidence to reject the null hypothesis