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 values a 5% 2.5% 1% critical z-values 1.65 1.96 2.58 what is (are) the critical value(s) for z in this study? –1.65 and 1.65 –1.96 and 1.96 1.65 1.96

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, we want to know if the two groups of teachers had different levels of job satisfaction.

Suppose that we have:

[tex]\mu_1[/tex] = mean of level of job satisfaction for first group of teachers.
[tex]\mu_2[/tex] = mean of level of job satisfaction for second group of teachers.

Then, as the test is for checking if the difference exist, the null hypothesis will deny existence of any difference.

Thus, we get:

Null hypothesis: [tex]H_0: \mu_1-\mu_2 = 0[/tex] or we say [tex]H_0: \mu_1 = \mu_2[/tex]
Alternate hypothesis: [tex]H_1: \mu_1-\mu_2 \neq 0[/tex] or we say [tex]H_1: \mu_1 \neq \mu_2[/tex]

The alternate hypothesis creates two regions, on either side as:

[tex]\mu_1 < \mu_2[/tex] and [tex]\mu_1 > \mu_2[/tex]

This is why it is two tailed test.

The level of significance is 5% specified.

Thus, [tex]\alpha = 5\% = 5/100 = 0.05[/tex]

From the critical values table, the critical value(s) of Z for level of significance 0.05 and for two tailed test are: [tex]\pm 1.96[/tex]

Thus, the critical values of Z in this study are given by: Option C: -1.96 and 1.96

Learn more about hypothesis testing here:

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