We are trying to ascertain in the proportion of people in the population with chronic back pain has changed as employment has shifted from more physical (construction, labor, manufacturing) to less physical in nature (service, office work, technology) over the years. In the US, 25% of the population reports having back pain in the past 12 months; this number has been constant for three decades. The General Social Survey, however, in 2002, reported 28% of people responding to the survey (n=1500) had chronic back pain in the last 12 months. Using the information above conduct a hypothesis test using an alpha level of 0.05.

1. Conduct a hypothesis test that assess whether the 2002 proportion of people with chronic back pain is truly higher than the population average. What is the alternative hypothesis?

a. 1: < 0.25 b. 1: < 0.28 c. 1: > 0.25 d. 1: > 0.28

2. Will you obtain your critical value from the t or the z distribution?

a. T Distribution b. Z Distribution

3. What is your critical value?

a. 1.65 b. 2.33 c. 1.96 d. 2.58

4. What is your test statistic?

a. 2.683 b. 2.788 c. 2.587 d. 2.451

5. What is your conclusion?

a. Fail to Reject the Null Hypothesis b. Reject the Null Hypothesis

On average, 80% of the population report having their activities limited by their health in the past 30 days. We conduct a survey of 26 people, and find that only 77% of our respondents report having their activities limited by their health in the past 30 days. Conduct a hypothesis test that our finding is truly lower than the population proportion of people who have had their activities limited by their health in the past 30 days. Use and alpha level of 0.05.

6. What is the alternative hypothesis?

a. 1: 0.77 b. 1: 0.80 c. 1: < 0.77 d. 1: < 0.80

7. What is your critical value?

a. -2.485 b. -1.708 c. -2.060 d. -1.703

8. What is your test statistic?

a. -0.375 b. -0.382 c. -0.453 d. -0.239

9. What is your conclusion?

a. Fail to Reject the Null Hypothesis b. Reject the Null Hypothesis

10. If we changed the alpha level of 0.01, would you make the same conclusion as you did above?

a. Yes b. No