Question

3. Do you see any striking difference between problem 1 and 2?

1. At a certain university, the mean income of parents of the entering class is reported to by $91,600. The president of another university feels that the parents’ income for her entering class is more than $91,600. She surveys 100 randomly selected families and finds the mean income to be $96,321. Given σ = $9555. With α = 0.05, is she correct?

1. State the null and alternative hypotheses which would be used to test the research hypothesis that the mean income is more than $91,600.

2. Use a significance level of a = .05. What is the rejection region?

3. Calculate the test statistic using the given sample mean.

4. Is there enough evidence to reject the null hypothesis?

5. What conclusion can be drawn about the income of the parents?

6. Find the p-value for your test statistic.

7. Do the test statistic and the p-value lead to the same conclusion?

2. At a certain university, the mean income of parents of the entering class is reported to by $91,600. To see how this compares to his university, a president surveys 28 randomly selected families and finds that their average income is $88,500 and standard deviation of the sample is $10,000. Can the president conclude that there is a difference? At α = 0.10, is he correct?

The sample data appear to come from an approximately normally distributed population.

a. State the null and alternative hypotheses which would be used to test the research hypothesis that the

    mean income is different from $91,600.

2. Use a significance level of a = .10. What is the rejection region?

3. Calculate the test statistic using the given sample mean.

4. Is there enough evidence to reject the null hypothesis?

5. What conclusion can be drawn about the income of the parents?

6. Find the p-value for your test statistic.

7. Do the test statistic and the p-value lead to the same conclusion?

Answer 1