A graduate student is performing a study on a new antidepressant. The drug is supposed to reduce depression, but the graduate student realizes that it may do nothing or even increase depression, so she decides to formulate nondirectional hypotheses and conduct a two-tailed test. She knows that the average score for all depressed people is = 15, with a standard deviation of = 4. If she designates the mean for the population of depressed people who take the antidepressant as antidepressantantidepressant, she can identify the null and alternative hypotheses as:

	H: antidepressantantidepressant=
	H: antidepressantantidepressant

The sample of 64 depressed people who tried out the new antidepressant scored an average of 14.1.

Since the graduate student knows the standard deviation of the scores on the depression inventory for the population of people who are depressed, she intends to use a hypothesis test that uses the z-score of the sample mean as the test statistic (also known as the z test). First, she wants to make sure all the required assumptions are satisfied. Which of the following conditions is nota required assumption for the z test?

Members of the sample are selected randomly.

Each member of the sample must be related in some way to at least one other member of the sample (as in a sibling, friend, or coworker).

The scores on the depression inventory follow a normal distribution or the sample size is large (at least 30).

The standard deviation of the scores on the depression inventory is the same for those who take the antidepressant and those who don't.

Each observation is independent of every other observation.

Use the Distributions tool to find the critical region for = 0.05.

Standard Normal Distribution

Mean = 0.0

Standard Deviation = 1.0

-4-3-2-101234z.2500.5000.2500-0.6740.674

The critical z-scores (the values for z-scores that separate the tails from the main body of the distribution, forming the critical regions) are .

Calculate the z statistic, and use the Distributions tool to evaluate the null hypothesis. The z statistic is . The z statistic lie in the critical region for a two-tailed hypothesis test. Therefore, the null hypothesis is .