Question

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

Explanation:

Step1: Determine Test Type

The study is comparing two groups (teachers who choose curriculum vs. those assigned resources) to see if there's a difference in job satisfaction. This is a two - tailed test because we are testing for a difference (not a one - sided greater or less than). For a two - tailed test with a significance level (\(\alpha\)) of 5% (\(\alpha = 0.05\)), we split the significance level into two tails, so \(\alpha/2=0.025\) for each tail.

Step2: Find Critical z - values

Looking at the table, for a two - tailed test with \(\alpha = 0.05\) (or \(\alpha/2 = 0.025\) in each tail), the critical z - values are the values corresponding to the 2.5% upper - tail and the - 2.5% lower - tail. From the table, the critical z - value for 2.5% upper - tail is 1.96, and for the lower - tail (since the normal distribution is symmetric), it is - 1.96. So the critical z - values are - 1.96 and 1.96.

Answer:

-1.96 and 1.96