# Hypothesis testing for one sample z test

There is a popular belief that herbal remedies such as ginkgo biloba and ginseng may improve learning and memory in healthy adults, these effects are usually not supported by well controlled research. in a typical study a researcher obtains a sample of n=16 participants and has each person take a herbal supplement for 90 days. at the end of the 90 days each person takes a standardized memory test. for the general population scores from the test form a normal distribution with a mean of u=50 and a standard deviation of o=12. the sample of research participants had a average of M=54.

Assuming a two tailed test, state the null hypothesis in a sentence that includes the two variables being examined.

* the herbal supplements have an increasing effect on memory scores. ?

* the herbal supplements have no effect on memory scores?

* the herbal supplements have a decreasing effect on memory scores?

using the symbols state the null hypothesis and the alternative hypothesis (assuming a two tailed test):________

using the standard four step procedure conduct a two tailed hypothesis test with o= .05 to evaluate the effect of the supplements.

z- critical = ____

z= ______

these results indicate

* rejection of the null hypothesis, the herbal supplements have a significant effect on memory scores

* rejection of the null hypothesis the herbal supplements do not have a significant effect on memory scores.

* failure to reject the null hypothesis, the herbal supplements have a significant effect on memory scores

* failure to reject the null hypothesis, the herbal supplement do not have a significant effect on memory scores.

https://brainmass.com/statistics/probability/hypothesis-testing-sample-test-584585

#### Solution Preview

1. Choose the herbal supplements have no effect on memory scores

2. ho: u=50 vs. ha: ...

#### Solution Summary

The solution gives detailed steps on explaining a hypothesis testing for a one sample z test.

T-Statistic and Z-Statistic and Small Test Samples

Please help answer the following question.

Why is a t-statistic as opposed to a z-statistic used to test small samples? Does the choice of test statistic alter how you employ the 5-step hypothesis testing procedure?

When testing two populations with small sample sizes, do both sample sizes have to be the same size?

When does the t-statistic approximate the z-statistic? What is the significance of the pictures at the top of the t-statistic table and the z-statistic table

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