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 = 0.05, should we reject $H_0$or should we fail to reject $H_0$?

Exercise 20

Short answer

a. The critical values are -1.96 and 1.96.

b. The decision of the statistical test is to fail to reject the null hypothesis.

Step-by-step solution

Given information

A test statistic value of $z=-1.94$ is obtained, and the claim to be tested is $p=\frac{3}{8}$.

Hypotheses and tail of the test

The hypotheses are as follows:

Null Hypothesis: $p=\frac{3}{8}$

Alternative Hypothesis: $p\ne \frac{3}{8}$

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

Critical value

a.

Referring to the standard normal table, 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 absolute value of the test statistic is greater than the critical value, then the null hypothesis is rejected; otherwise, not.

Since the absolute value of the test statistic is less than the critical value, the decision is to fail to reject the null hypothesis.