Question

Suppose you wish to perform a hypothesis test for a population mean. Suppose that the population standard deviation is known, the population distribution is Normal, and the sample is small. Would you perform a z-test or t-test?

a.The z-test is appropriate.

b.Either test is appropriate.

c.The t-test is appropriate.

d.Neither test is appropriate.

Answer 1

The correct option is a. The z-test is appropriate. [ANSWER]

Explanation:

We need ot perform a hypothesis test for a population mean.

Now, we know that we use the z-test when the following conditions are satisfied:

1. The population distribution is normal.

2. Either the population standard deviation is known or the sample is large.

Moreover, a t-test is appropriate when the following conditions are satisfied:

1. The population distribution is normal.

2. The population standard deviation is not known.

3. The sample size is small.

Now, for the given population, the distribution is normal and the population standard deviation is known thus a z-test is appropriate (irrespective of the small sample size) and the correct option is a.

The t-test is not appropriate here since it is used when population standard deviation is not known but here we know the the value of the population standard deviation.

Option b. is not correct because both the tests are not appropriate as t-test is not appropriate in this situation.

Option c. is not correct because the t-test is not appropriate here as explained above.

Option d. is not correct because z-test is appropriate here.

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