Q1. Please use the following for the next 7 questions. A random sample of 172 students was asked to rate on a scale to from 1 (not important) to 5 (extremely important) health benefits as a job characteristic (note that the rating scale can also have decimals, i.e. a student can give a rating of 1.32). The sample mean rating was 3.31, and the sample standard deviation was 0.70. For a type I error of 1% (alpha), can you be reasonably certain that the average rating is more than 3 in the population?

State the null and alternative hypotheses.

H0: = 0, Ha: > 3.31

H0: = 0, Ha: < 3.31

H0: = 0, Ha: > 3

H0: = 0, Ha: 3

2. Specify the rejection region for= 0.01. Reject H0 if

z > 2.33

t > 2.32

z < 2.33

t < 2.32

3. Calculate the test statistic

2.3

-5.8

0.44

5.8

4. What is your conclusion?

Reject H0

Fail to Reject H0

Reject Ha

Fail to reject Ha

5. Obtain the lower bound of a 99% confidence interval for the mean rating.

0.31

0.34

3.44

3.17

6. Obtain the upper bound of a 99% confidence interval for the mean rating.

0.31

0.34

3.44

3.17

7. What assumption(s) do you need to make in order to answer the above questions?

No assumptions are needed

The population distribution is assumed to be normal.

The population distribution is assumed to be t-distributed.

The sampling distribution of the sample is assumed to be normal.