Inference Test (Benchmark #3)

1. Inference Test (Benchmark #3) On a sheet of paper, number it #1-8. Your goal is to determine which main formula/branch you will use to solve (identifying test type).

2. Suppose you have a theory that only children have higher cholesterol than children who have siblings. The average cholesterol level for all Americans is 190. You take a sample of 100 only children and find that their cholesterol is 198 with a standard deviation of 15. At the 5% significance level, do only children have significantly higher cholesterol levels?

3. According to an April 2013 CNN Poll, a poll of 1012 people showed that 617 believed that the U.S. should intervene if North Korea attacked South Korea. Find a 95% confidence interval for the true proportion of Americans who believe that U.S. should intervene if North Korea attacks South Korea.

4. Dr. Raj has invented a new preservative for cut flowers and wants to test its effectiveness against the leading commercial preservative. He took two random samples of 100 cut carnations each. One group of flowers was set in vases containing the new preservative and the other group was set in vases containing the commercial preservative. The flowers in the new preservative began to wilt after an average of 75 hours with a standard deviation of 15 hours. For the flowers in the commercial preservative the average was 71 hours with a standard deviation of 10 hours. Is the data statistically significant evidence that the new preservative is more effective? Use a 5% significance level.

5. A simple random sample of 75 high school seniors who had after-school jobs showed an average hourly wage of $8.75 with a standard deviation of $0.50. Find a 95% confidence interval for the average hourly wage of all high school seniors who had after-school jobs. • (Please respond in sentence form – round to the nearest cent.)

6. If we would like to create a poll with the following margin of errors, how many people should our simple random sample contain? +/- 7%

7. The State Fish and Game Division claims that 75% of the fish in the Swatara Creek are Rainbow Trout. However, the local fishing club caught and released 189 fish one weekend and found that 125 were Rainbow Trout. Does this indicate that the percentage of Rainbow Trout in the Creek is less than 75%?

8. Late-night truck drivers sometimes take an over-the-counter non-prescription drug to keep them from falling asleep. The main ingredient is caffeine, but too much caffeine may not be too good for a person’s health. A random sample of eight truck drivers agreed to have their pulse rate (beats per minute) measured one-half hour before and one-half hour after taking such a drug. The results are shown in the accompanying table. Use a 1% significance level to test the claim that the pulse rate per minute will be different for all truck drivers taking the drug.

9. An experiment is conducted investigating the long-term effects of early childhood intervention programs (such as head start). In one (hypothetical) experiment, the high-school drop out rate of the experimental group (which attended the early childhood program) and the control group (which did not) were compared. In the experimental group, 73 of 85 students graduated from high school. In the control group, only 43 of 82 students graduated. Is this difference statistically significant?