Question: There is some evidence to suggest that certain herbs can have an effect on human memory. A researcher plans to use a standardized memory test to evaluate the effect of the herbs. Scores on the standardized test form a normal-shaped distribution with a mean of \(\mu=70\) and a standard deviation of \(\sigma=15\). The researcher obtains a sample of \(n=25\) people and has each person take an herbal supplement every day for 30 days. At the end of the 30 -day period, each person takes the standardized memory test and the mean score for the sample is calculated to be \(M=78\).

1. In a sentence, state the null hypothesis for this test.
2. Using symbols, state the null hypothesis and the alternative hypothesis.
3. Identify the critical region for the test assuming that the researcher is using \(\alpha=.05\).
4. Calculate the \(z\) -score statistic for the sample.
5. What decision should the researcher make about the null hypothesis?
6. What decision should the researcher make about the effect of the herbal supplement?

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