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Chapter 8: Q23 (page 372)

Critical Values. In Exercises 21鈥�24, refer to the information in the given exercise and do the following.

a. Find the critical value(s).

b. Using a significance level of 伪= 0.05, should we reject H0or should we fail to reject H0?

Exercise 19

Short Answer

Expert verified

a. The critical values are -1.96 and 1.96.

b. The null hypothesis is rejected.

Step by step solution

01

Given information

A test statistic value of z=2.01 is obtained, and the claim to be tested is p鈮�0.345.

02

Hypotheses and tail of the test

In correspondence with the given claim, the following hypotheses are set up:

Null Hypothesis: p=0.345

Alternative Hypothesis: p鈮�0.345

Since there is a not equal sign in the alternative hypothesis, the test is two-tailed.

03

Critical value

a.

The critical values of z corresponding to the two-tailed test at 伪=0.05are -1.96 and 1.96.

04

Decision about the test

b.

If the test statistic value does not lie between the critical values, then the null hypothesis is rejected.

Here, the value of the test statistic (2.01) does not lie between the critical values (greater than 1.96). Thus, the null hypothesis is rejected.

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