Question

The following graph portrays the decision criterion for a onemean z-test, using the critical-value approach to hypothesis testing. The curve in the graph is the normal curve for the test statistic under the assumption that the null hypothesis is true.

Determine the

a. rejection region.

b. nonrejection region.

c. critical value(s).

d. significance level.

e. Draw a graph that depicts the answers that you obtained in parts (a)-(d).

f. Classify the hypothesis test as two tailed, left tailed, or right tailed.

Short answer

(a) The rejection region is $z\ge 1.28$

(b) The non- rejection region is z < 1.28

(c) The critical value is 1.28

(d) The significance level is 0.10

Step-by-step solution

Subpart (a) Step 1:

(a)

The rejection zone in this example consists of all z-scores to the right of 1.28. The zone of rejection is:$z\ge 1.28$

Subpart (b) step 1:

(b)

The non-rejection zone in this situation is defined as all z-scores to the left of 1.28. The non-rejection zone is defined as:$z<1.28$

Subpart (c) Step 3:

(c)

The rejection and non-rejection areas are separated by the crucial value of 1.28.

Subpart (d) Step 1:

(d)

The region to the right of the 1.28 is the significance level. The significance threshold in this example is 0.10.

Subpart (e) Step 1:

Subpart (f) step 1:

(f)

The provided hypothesis test is a right tailed test since the rejection zone is to the right of the critical value.