Question

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

a. Find the critical value(s).

b. Using a significance level of \(\alpha \)= 0.05, should we reject \({H_0}\)or should we fail to reject \({H_0}\)?

Exercise 19

Short answer

a.The critical values are -1.96 and 1.96.

b.The null hypothesis is rejected.

Step-by-step solution

Given information

A test statistic value of \(z = 2.01\) is obtained, and the claim to be tested is \(p \ne 0.345\).

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:\(p \ne 0.345\)

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

Critical value

a.

The critical values of z corresponding to the two-tailed test at \(\alpha = 0.05\)are -1.96 and 1.96.

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.