Question

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

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

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

(c) Since $\alpha =0.01$. 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 $\alpha =0.01$. 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 $\alpha =0.01$. 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 $\alpha =0.01$. 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.