Exercises Intro to hypothesis Testing
1. Define the critical region for a hypothesis test, and explain how the critical region is related to the alpha level.
2. The term error is used in two different ways in hypothesis testing: a Type I error (or Type II) and the standard error.
a. What can a researcher do to influence the size of the standard error? Does this action have any effect on the probability o
b. What can a researcher do to influence the probability of a Type I error? Does this action have any effect on the size of the standard error?
3. Some researchers claim that herbal supplements such as ginseng or ginkgo biloba enhance human memory. To test this claim, a researcher selects a sample of n = 25 college students. Each student is given a ginkgo biloba supplement daily for six weeks and then all the participants are given a standardized memory test. For the population, scores on the test are normally distributed with μ = 70 and s = 15. The sample of n = 25 students had a mean score of M = 75.
a. Are the data sufficient to that the herb has a significant effect on memory? Use a two-tailed test with α = .05.
b. Compute Cohen’s d for this study.
4. A researcher would like to determine whether a new tax on cigarettes has had any effect on people’s behavior. During the year before the tax was imposed, stores located in rest areas on the state thruway reported selling an average of µ = 410 packs per day with s = 60. The distribution of daily sales was approximately normal. For a sample of n = 9 days following the new tax, the researcher found an average of M = 386 packs per day for the same stores.
a. Is the sample mean sufficient to conclude that there was a significant change in cigarette purchases after the new tax. Use a two-tailed test with α = .05.
b. If the population standard deviation was s = 30, is the result sufficient to conclude that there is a significant difference?
c. Explain why the two tests lead to different outcomes.
5. A researcher is testing the effectiveness of a new herbal supplement that claims to improve physical fitness. A sample of n = 16 college students is obtained and each student takes the supplement daily for six weeks. At the end of the 6-week period, each student is given a standardized fitness test and the average score for the sample is M = 39. For the general population of college students, the distribution of test scores is normal with a mean of µ = 35 and a standard deviation of s = 12. Do students taking the supplement have significantly better fitness scores? Use a one-tailed test with α = .05.
6. A researcher selects a sample of n = 25 from a normal population with µ = 40 and s = 10. If the treatment is expected to increase scores by 3 points, what is the power of a two-tailed hypothesis test using α = .05.