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Chapter 8: Que. 1 (page 392)

Explain the meaning of each term.

a. null hypothesis b. alternative hypothesis

c. test static d. significance level

Short Answer

Expert verified

a). The null hypothesis is a hypothesis to be tested.

b). The alternative hypothesis is a hypothesis which contradicts the null hypothesis.

c). The test statistic is statistic used as a basis for deciding whether the null hypothesis should be rejected.

d). The significance level of the hypothesis test is the probability of making a Type I error, that is, of rejecting a true null hypothesis.

Step by step solution

01

Step 1. Definition (a).

Null hypothesis:

The null hypothesis is a hypothesis to be tested. We use symbol H0to represent the null hypothesis.

02

Step 2.  Definition (b).

Alternative hypothesis:

The alternative hypothesis is a hypothesis which contradicts the null hypothesis. A hypothesis is considered to be alternative to the null hypothesis. We use the symbol Hato represent the alternative hypothesis.

03

Step 3. Definition (c).

Test statistic:

It is used as a basis for deciding whether the null hypothesis should be rejected or not.

04

Step 4. Definition (d).

Significance level:

It is the probability test, making a Type I error, that is, of rejecting a true null hypothesis.

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Most popular questions from this chapter

PowerFor a hypothesis test with a specified significance level , the probability of a type I error is, whereas the probability of a type II error depends on the particular value ofpthat is used as an alternative to the null hypothesis.

a.Using an alternative hypothesis ofp< 0.4, using a sample size ofn= 50, and assumingthat the true value ofpis 0.25, find the power of the test. See Exercise 34 “Calculating Power”in Section 8-1. [Hint:Use the valuesp= 0.25 andpq/n= (0.25)(0.75)/50.]

b.Find the value of , the probability of making a type II error.

c.Given the conditions cited in part (a), find the power of the test. What does the power tell us about the effectiveness of the test?

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