A study investigated the job satisfaction of teachers allowed to choose supplementary curriculum for their classes versus teachers who were assigned all curricular resources for use in their classes. The authors of the study wanted to know if the two groups of teachers had different levels of job satisfaction. They will use a significance level of 5% for their test.
Upper-Tail Valuesa5%2.5%1%Criticalz-values1.65 1.962.58What is (are) the critical value(s) for z in this study?a. 1.65 and 1.65b. 1.96 and 1.96c. 1.65d. 1.96

Correct option: (b) -1.96 and 1.96.

Step-by-step explanation:

In this case the researchers wants to determine whether there is a difference between the levels of job satisfaction for the two groups of teachers.

The groups are divided as follows:

Group 1: teachers are allowed to choose supplementary curriculum for their classes

Group 2: teachers were assigned all curricular resources for use in their classes.

The hypothesis to perform this test is defined as follows:

H₀: There is no difference between the levels of job satisfaction for the two groups of teachers, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a significant difference between the levels of job satisfaction for the two groups of teachers, i.e. μ₁ - μ₂ ≠ 0.

The hypothesis defined suggests that the test is two-tailed, i.e. there are two rejection region.

The significance level of the test is, α = 0.05.

The z-test is used to perform the test.

Then the rejection regions are defined as follows:

Use the z-table for the two critical values as follows:

Thus, the critical value of z are -1.96 and 1.96.

Thus, the correct option is (b).