Each of the following situations calls for a significance test. State the appropriate null hypothesis Ho and alternative hypothesis Ha in each case. Be sure to define your parameter each time.

Each of the following situations calls for a significance test. State the appropriate null hypothesis Ho and alternative hypothesis Ha in each case. Be sure to define your parameter each time.

A. Matt's car averages 26 miles per gallon on the highway. He switches to a new brand of motor oil that is advertised to increase gas mileage. After driving 3000 highway miles with the new oil, he wants to determine if the average gas mileage has increased.

B. A June 2010 Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they rarely or never argue with their friends. You wonder whether this national result would be true in your school. So you conduct your own survey of a random sample of students at your school.

2. Here are several situations where there is an incorrect application of the ideas presented I this section. Explain what is wrong in each situation and why it is wrong.

A. A change is made that should improve student satisfaction with the parking situation at your school. The null hypothesis, that there is an improvement, is tested versus the alternative, that there is not change.

B. A researcher test the following null hypothesis: Ho:

C. A climatologist wants to test the null hypothesis that it will rain tomorrow.

3. A test of the null hypothesis Ho: p = .25 gives a test statistic z = 1.6.

A. What is the p-value if the alternative is Ha: p > .25?

B. What is the p-value if the alternative is Ha: p < .25?

C. What is the p-value if the alternative is Ha: p .25?

4. A research report described the results of two studies. The P-value for the first study was 0.049; for the second it was 0.00002. Conduct a few sentences comparing what these P-values tell you.

5. In a recent year, 73% of first-year college students responding to a national survey identified "being very well-off financially" as an important personal goal. A state university finds that 132 of an SRS of 200 of its first-year students say that this goal is important.

A. Is there good evidence that the proportion of all first-year students at this university who think being very well-off is important differs from the national value, 73%? Carry out a significance test to help answer this question.

B. Construct and Interpret a 95% confidence interval for the proportion of all first-year

students at the university who would identify being well-off as an important personal goal. What additional information does the confidence interval provide?