Question

This exercise contain graphs portraying the decision criterion for a one-mean 2-test. The curve in each graph is the normal curve for the test statistic under the assumption that the null hypothesis is true. For each exercise, determine the

a. rejection region.

c. critical value(s).

b. nonrejection region.

d. significance level.

e. Construct a graph similar to that in Fig. 9.3 on page 361 that depicts your results from parts (a)-(d).

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

Short answer

(a) The rejection region is z>1.645.

(b) The non rejection region is z ≤1.645.

(c)For the given graph, z=1.645 is the value which separates critical and non critical regions.

(d) The significance level is 0.05.

(e)

(f) As there is only one critical region towards right , the corresponding test is right -test failed.

Step-by-step solution

Step 1. Given

The curve in each graph is the normal curve for the test statistic under the assumption that the null hypothesis is true.

Part(a) Step 2. Determine the rejection region

The rejection region for the above graph is the set of values of z which are greater than 1.645. That is, the rejection region is z>1.645.

Part (b) Step 3.  Determine the non-rejection region 

The non-rejection region for the above graph is the set of values of z which are less than 1.645. That is, the non rejection region is z ≤1.645.

Part(c) Step 4. Determine the critical values.

The critical value is the value of test statistic that separate the rejection and non rejection regions. For the given graph, z=1.645 is the value which separates critical and non critical regions.

Part( d) Step 5. Determine the significance level

The size of critical region is known as significance level. For the given graph, the size of critical region is 0.05.

Hence, the significance level is 0.05.

Part(e) Step 6. Construct a graph similar to that in Fig. 9.3 on page 361 that depicts your results from parts (a)-(d). 

The graph that depicts critical region, non critical region and critical value is shown below:

Part (f) Step 7. Identify the hypothesis test as two tailed, left tailed or right tailed.

As there is only one critical region towards right , the corresponding test is right -test failed.