Some researchers claim that herbal supplements (such as ginkgo biloba) can impact 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 with σ = 15. The sample of n = 25 students had a mean score of M = 76.a. Are the data sufficient to demonstrate that the herb has a significant effect on memory? Use a two-tailed test with
α
= 0.05.

b. Compute Cohen's d for this study.

(a) The data are not sufficient to demonstrate that the herb has a significant effect on memory.

(b) Cohen's d = 5.07

Step-by-step explanation:

(a) Null hypothesis: The herbal supplement (ginkgo biloba) can impact human memory

Alternate hypothesis: The herbal supplement (ginkgo biloba) cannot impact human memory.

Z = (sample mean - population mean) ÷ sd/√n

Sample mean = 76, population mean = 70, sd = 15, n = 25

Z = (76 - 70) ÷ 15/√25 = 6 ÷ 3 = 2

Using a 0.05 significance level for a two tailed test, the critical value is 1.96

For a two tailed test, the region of no rejection of the null hypothesis lies between -1.96 and 1.96

Conclusion: Since the test statistic (Z = 2) falls outside the region bounded by -1.96 and 1.96, reject the null hypothesis. The herbal supplement (ginkgo biloba) cannot impact human memory.

Hence, the data are not sufficient to demonstrate that the herb has a significant effect on memory.

(b) Cohen's d = M/sd = 76/15 = 5.07

step-by-step explanation:

you divide the denominator by the numerator on both sides and if the quotients are equal then the fractions are equivalent