1. Last fall, a sample of n = 25 freshmen was selected to participate in a new 4-hour training program designed to improve study skills. To evaluate the effectiveness of the new program, the sample was compared with the rest of the freshman class. All freshman must take the same English Language Skills course, and the mean score on the final exam for the entire freshman class was μ = 74. The students in the new program had a mean score of M = 78 with SS = 2400. a. On the basis of these data, can the college conclude that the students in the new program performed significantly better than the rest of the freshman class? Use a one-tailed test with α = .05. b. Can the college conclude that the students in the new program are significantly different from the rest of the freshman class? Use a two-tailed test with α = .05. 2. The herbal supplement ginkgo biloba is advertised as producing an increase in physical strength and stamina. To test this claim, a sample of n = 36 adults is obtained and each person is instructed to take the regular dose of the herb for a period of 30 days. At the end of 30-day period, each person is tested on a standard treadmill task for which the average, age-adjusted score is μ = 55. The individuals in the sample produce a mean score of M = 58.5 SS = 5040. a. Are these data sufficient to conclude that the herb has a statistically significant effect using a two-tailed test with α = .05? b. What decision would be made if the researcher used a one-tailed test with α = .05? (Assume that the herb is expected to increase scores.) 3. When adults are given a set of items to hold in memory, they automatically rehearse the items to prevent forgetting. Young children, however, do not spontaneously use rehearsal. As a result, when given a small set of items to remember, 2-year-old children on average can recall only μ = 2 items. A researcher would like to determine whether memory can be improved by teaching 2-year-old children to use rehearsal. A sample of n = 16 children is obtained and the children are trained to use rehearsal during a memory task. After training, the children in the sample show an average recall of M =4.3 items, with SS = 60. a. Use a one-tailed test with α = .05 to determine whether the data are sufficient to conclude that the rehearsal training produces a significant increase in memory. b. Compute Cohen’s d and r2 for these data to measure the effect size.
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