To determine the critical value(s) for [tex]\( z \)[/tex] in this study, we'll begin by noting the significance level used, which is 5% (or 0.05). The study aims to compare job satisfaction between two groups of teachers, which suggests that the authors want to know if there are any differences in job satisfaction levels. Typically, such a scenario involves a two-tailed test where differences can occur in either direction (higher or lower job satisfaction).
For a two-tailed test, we need to find the critical values that correspond to the significance level of 5%. This means we will split the 5% significance level into two tails, each containing 2.5% (0.025) of the total area under the standard normal curve.
Given the provided table of upper-tail critical z-values, corresponding to different significance levels, we can identify the appropriate values:
- For a 5% significance level in a one-tailed test, the critical z-value is 1.65.
- For a 2.5% significance level in a one-tailed test, the critical z-value is 1.96.
- For a 1% significance level in a one-tailed test, the critical z-value is 2.58.
However, since our test is two-tailed, we look at the critical values for both tails:
- The positive critical value for the upper tail (one-tail) at 5% significance is 1.65.
- For the lower tail in a two-tailed test, the critical value would be the negative counterpart, which is -1.65.
Therefore, for a two-tailed test at a 5% significance level, the critical z-values would be -1.65 and 1.65.
So, the critical values for [tex]\( z \)[/tex] in this study are: [tex]\(\boxed{-1.65 \text{ and } 1.65}\)[/tex].
