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 regions are z<-1.96 and z>1.96..

(b) The non rejection region is -1.96 <z<1.96

(c)The critical values for the test are z=-1.96 and 2, = 1.96

(d) The significance level is 0.05.

(e)

(f)Here the hypothesis is two-tailed test.

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

From the above graph it is clear that is that the rejection regions are z<-1.96 and z>1.96.

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

From the above graph it is clear that the nonrejection region is -1.96 <z<1.96

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

The critical values for the test are z=-1.96 and 2, = 1.96

Part( d) Step 5. Determine the significance level

The graph shows the critical region in the two tails so if we add the area under the rejection region we get the significance level. That is,

a=0.025+0.025.

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.

Here the hypothesis is two-tailed test.