Question

Answer the following questions:

What is the difference between two samples that are dependent and two samples that are independent? Give an example of each.

Explain how to perform a two-sample z-test for the difference between the means of two populations using large independent samples.

What conditions are necessary in order to use the z-test to test the difference between two population means?

Answer 1

Two samples are independent if the sample values selected from one population are not related or somehow paired or matched with the sample values selected from the other population. Two samples are dependent if the members of one sample can be used to determine the members of the other sample.

Steps to perform a two-sample z test

1. Write the null hypothesis and alternative hypothesis ; then identify the claim.

2. Specify the level of significance.

3. Sketch the sampling distribution, add the test statistic, critical value(s) and rejection region(s).

4. Determine the critical value(s).

5. Determine the rejection region(s).

6. Calculate the standardized test statistic z.

7. Make a decision to reject or fail to reject .

(a) If z is in the rejection region - reject .

(b) If z is not in the rejection region - fail to reject .

8. Interpret the decision in the context of the original claim

Three conditions must be satisfied to perform this z-test.

• The two samples must be independent. Two samples are independent if the sample values selected from one population are not related to or somehow paired with the sample values selected from the other population.

• Each sample size must be at least 30 or, if not, each population must have a normal distribution with a known standard deviation.

• The samples must be randomly selected