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Chapter 8: Q. 9.39 (page 364)

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

Expert verified


(a) The rejection regions arez<-1.645andz>1.645

(b) The non rejection region is-1.645<z<1.645

(c)The critical values for the test are z0=-1.645andz0=1.645

(d) The significance level is 0.10.

(e)

(f) The hypothesis is two-tailed test.

Step by step solution

01

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.

02

Part(a) Step 2. Determine the rejection region

From the above graph it is clear that is that the rejection regions arez<-1.645andz>1.645

03

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

From the above graph it is clear that is that the non- rejection regions are-1.645<z<1.645

04

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

The critical values for the test arez0=-1.645andz0=1.645

05

Part( d) Step 5. Determine the significance level

The graph shows the critical region in the two-tail so the area under the rejection region is the significance level. That is,

α=0.05+0.05=0.10

06

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:

07

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

The hypothesis is two-tailed test.

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