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8th Edition

Charles Henry Brase + 1 other

Publisher: Cengage Learning

ISBN: 9781337558075

Chapter 9, Problem 1CR

Textbook Problem

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**Terminology** Answer each of the following statements true or false regarding the *level of significance a* of a hypothesis test.

(i) The level of significance is the probability of rejecting the null hypothesis when it is in fact true.

(ii)The level of significance of a test depends on the value of the sample test statistic.

(iii)The level of significance is generally set in advance before samples are drawn.

(iv)The level of significance depends on the alternate hypothesis.

(v) The level of significance of a test depends on the sample size.

**(i)**

To determine

The statement “The level of significance is the probability of rejecting the null hypothesis when it is in fact true.” is true or false.

**Solution:** The statement “The level of significance is the probability of rejecting the null hypothesis when it is in fact true.” is true.

The level of significance is the probability of rejecting the null hypothesis when it is in fact true is true. This is the probability of type I error when we reject the null hypothesis.

**(ii)**

To determine

The statement “The level of significance of a test depends on the value of the sample test statistic.” is true or false.

**Solution:** The statement “The level of significance of a test depends on the value of the sample test statistic.” is false.

The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. Hence the level of significance of a test does not depend on the value of the sample test statistic.

**(iii)**

To determine

The statement “The level of significance is generally set in advance before samples are drawn.” is true or false.

**Solution:** The statement “The level of significance is generally set in advance before samples are drawn.” is true.

The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. Hence the statement “The level of significance is generally set in advance before samples are drawn.” is true.

**(iv)**

To determine

The statement “The level of significance depends on the alternate hypothesis.” is true or false.

**Solution:** The statement “The level of significance depends on the alternate hypothesis” is false.

The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. The statement “The level of significance depends on the alternate hypothesis” is false.

**(v)**

To determine

The statement “The level of significance of a test depends on the sample size.” is true or false.

**Solution:** The statement “The level of significance of a test depends on the sample size.” is false.

The level of significance is determined by the researcher before conducting the experiment. The significance level decides whether to reject the alternate hypothesis or not. The statement “The level of significance of a test depends on the sample size.” is false.

Understanding Basic Statistics

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