Question

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 = 20 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 = 75 and σ = 15. The sample of n = 20 students had a mean score of M = 85.

Can the researcher conclude that scores on the memory test are significantly different after taking the supplement? Use a two-tailed test with α = .05. Be sure to state your null hypothesis, a decision about that null hypothesis, and a conclusion explaining your results with an APA format statement. Calculate Cohen’s d if necessary.

Answer 1

TWO TAILED TEST

The hypotheses are

$Ho:\mu=75$

$Ha:\mu\neq75$

Rejection region:

Reject Ho if Z > Z_0.025=1.96

Test statistics:

$Z=\frac{M-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{85-75}{\frac{15}{\sqrt{20}}}=2.98$

P value :

P value associated with Z statistic here calculated either using Z table or by Calculator as

0.0029

Conclusion:

Since Z> Z(0.025) and P-value is less than the level of significance(0.05), hence we reject the null hypothesis and conclude that at 0.05 level of significance we have enough evidence to support the claim.