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

Still missing data: means, SD?

To compare the job satisfaction levels of the two groups of teachers, the authors of the study will likely use a hypothesis test. The null hypothesis in this case would be that there is no difference in job satisfaction between the teachers who choose supplementary curriculum and those who are assigned all curricular resources. The alternative hypothesis would be that there is a difference in job satisfaction between the two groups.

To conduct the hypothesis test, the authors will need to calculate a test statistic and compare it to a critical value. The test statistic they will use depends on the type of data they have and the assumptions they make.

In this scenario, it seems like the authors might be comparing means or proportions between two groups. If they are comparing means (e.g., average job satisfaction scores), they might use a t-test. If they are comparing proportions (e.g., the proportion of satisfied teachers), they might use a chi-square test.

However, based on the information provided, it is not clear which test statistic the authors will use. The critical values you provided, which are z-values, suggest that they might be using a normal distribution as an approximation. The specific critical values you mentioned are for an upper-tail test (where the alternative hypothesis is that one group has a higher job satisfaction than the other). The 5% critical value (2.58) indicates that if the test statistic falls above this value, the authors would reject the null hypothesis at a 5% significance level.

Without more information about the data and assumptions, it is difficult to provide a definitive answer. However, based on the critical values you provided, it seems like the authors are conducting an upper-tail test using a z-test or a normal approximation.