Question

20. 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 = 28 college students. Each student is given a ginkgo biloba supplement daily for 6 weeks and then all of the participants are given a standardized memory test. Scores on the standardized test are μ = 80 and standard deviation of 15. The sample of 28 students had a mean score of M = 85. (8 points)
    1. Do the data indicate a significant effect of the herb on memory? Use a two-tailed test with α = 0.05. (Show all steps.)
    2. Compute Cohen's d to measure the size of the effect IF it exists.
    3. Write a sentence describing the outcome of the hypothesis test as it would appear in a research report.

Answer 1

This is a hypothesis testing for population mean. We assume that the sample is random and independent and come from a normal distribution.

We will use a 2 - tailed z - test

Null hypothesis: Herbal supplements such as ginseng or ginkgo biloba have no effect on human memory

Alternative Hypothesis:Herbal supplements such as ginseng or ginkgo biloba have an effect on human memory

VS

We use a z - test be the population standard deviation is known

n= 28  

Test statistic:

  

= 1.763

Critical Value at 0.05 level

Decision criteria: Reject null hypo if T.S. > C.V.

Since T.S. < C.V.

Decision: Do not reject null hypo at 0.05 level of significance. We conclude that the herbal supplements have no effect on human memory.

Cohen's d tells about the effect size if there is a difference between two data sets. Since we concluded that there is no effect (no difference) we can say that cohen's d does not exist.