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6. An example of a hypothesis test and the required assumptions 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 he decides to formulate nondirectional hypotheses and conduct a two-tailed test. He knows that the average score for all depressed people is ?? = 25, with a standard deviation of ? = 6. If he designates the mean for the population of depressed people who take the antidepressant as ?antidepressant, he can identify the null and alternative hypotheses as: H?: ?antidepressant = ?? H?: ?antidepressant ? ?? The sample of 36 depressed people who tried out the new antidepressant scored an average of 23.3. Since the graduate student knows the standard deviation of the scores on the depression inventory for the population of people who are depressed, he 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, he wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test? ? Each observation is independent of every other observation. ? 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 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). ? Members of the sample are selected randomly. Use the Distributions tool to find the critical region for ? = 0.05. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 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 .

6. An example of a hypothesis test and the required assumptions

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 he decides to formulate nondirectional hypotheses and conduct a two-tailed test. He knows that the average score for all depressed people is ?? = 25, with a standard deviation of ? = 6. If he designates the mean for the population of depressed people who take the antidepressant as ?antidepressant, he can identify the null and alternative hypotheses as:

H?: ?antidepressant = ??
H?: ?antidepressant ? ??

The sample of 36 depressed people who tried out the new antidepressant scored an average of 23.3.

Since the graduate student knows the standard deviation of the scores on the depression inventory for the population of people who are depressed, he 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, he wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test?

? Each observation is independent of every other observation.

? 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 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).

? Members of the sample are selected randomly.

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

Standard Normal Distribution
Mean = 0.0
Standard Deviation = 1.0

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 .

6. An example of a hypothesis test and the required assumptions

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 he decides to formulate nondirectional hypotheses and conduct a two-tailed test. He knows that the average score for all depressed people is ?? = 25, with a standard deviation of ? = 6. If he designates the mean for the population of depressed people who take the antidepressant as ?antidepressant, he can identify the null and alternative hypotheses as:

H?: ?antidepressant = ??
H?: ?antidepressant ? ??

The sample of 36 depressed people who tried out the new antidepressant scored an average of 23.3.

Since the graduate student knows the standard deviation of the scores on the depression inventory for the population of people who are depressed, he 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, he wants to make sure all the required assumptions are satisfied. Which of the following conditions is not a required assumption for the z test?

? Each observation is independent of every other observation.

? 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 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).

? Members of the sample are selected randomly.

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

Standard Normal Distribution
Mean = 0.0
Standard Deviation = 1.0

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 .

Added by Anthony T.

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