Although there is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well-controlled research (Persson, Bringlov, Nilsson, & Nyberg, 2004). In a typical study, a researcher obtains a sample of n = 36 participants and has each person take the herbal supplements every day for 90 days. At the end of the 90 days, each person takes a standardized memory test. For the general population, scores from the test are normally distributed with a mean of µ = 80 and a standard deviation of σ = 18. The sample of research participants had an average of M = 84.

a. Assuming a two-tailed test, state the null hypothesis in a sentence that includes the two variables being examined.

b. Using symbols, state the hypotheses (H0 and H1) for the two-tailed test.

c. Sketch the appropriate distribution, and locate the critical region for α = .05.

d. Calculate the test statistic (z-score) for the sample.

e. What decision should be made about the null hypothesis, and what decision should be made about the effect of the herbal supplements?