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 = 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 m = 70 and s = 15. The sample of n = 25 students had a mean score of M = 75. Are the data sufficient to that the herb has a significant effect on memory? Use a two-tailed test with a = .05.

Null Hypothesis:

Alternative Hypothesis:

Locate the critical region:

What is the result of the z test?

Reject or Fail to reject the null:

Answer 1

Here claim is that the herb has a significant effect on memory.

So hypothesis is vs

Her population standard deviation is known so we will use z test

The z-critical values for a two-tailed test, for a significance level of α=0.05

zc​=−1.96 and zc​=1.96

Graphically

Test statistics is

As test statistics do not fall in the rejection region, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that the herb has a significant effect on memory