Chapter 9: Q.10 (page 392)

Determine the critical value(s) for a one-mean z-test at the 1 % significance level if the test is
a. right tailed.
b. left tailed.
c. two tailed.

Short Answer

Expert verified

(a) Since $α = 0.01$ . The critical value of $z_{0.01} = 2.33$ is found in normal distribution tables, as illustrated in the image.

(b) Since $α = 0.01$ . The critical value of $- z_{0.01} = - 2.33$ is found in normal distribution tables, as illustrated in the image.

(c) Since $α = 0.01$ . The critical value of $\pm z_{\frac{0.01}{2}} = \pm z_{0.005} = 2.575$ is found in normal distribution tables, as illustrated in the image.

Step by step solution

Subpart (a) Step 1:

(a)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since $α = 0.01$ . The critical value of $z_{0.01} = 2.33$ is found in normal distribution tables, as illustrated in the image.

Subpart (b) Step 1:

(b)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since $α = 0.01$ . The critical value of $- z_{0.01} = - 2.33$ is found in normal distribution tables, as illustrated in the image.

Subpart (c) Step 1:

(c)

If the test is right tailed, we find the crucial value for a one-mean z-test at the 1% significance level.

Since $α = 0.01$ . The critical value of $\pm z_{\frac{0.01}{2}} = \pm z_{0.005} = \pm 2.575$ is found in normal distribution tables, as illustrated in the image.