Question

A researcher conducts an F-test and obtains a F-value of 2.36. The critical value with an alpha=.05 is 3.56. The researcher should:

1) reject the null hypothesis.
2) conduct a chi-square test.
3) fail to reject the null hypothesis.
4) conduct a t-test for each pair of means.

Answer 1

The researcher should fail to reject the null hypothesis since the obtained F-value of 2.36 is lower than the critical value of 3.56 at the α=0.05 significance level.

Step-by-step explanation:

When a researcher conducts an F-test and obtains an F-value that is lower than the critical value at a given significance level, the correct decision is to fail to reject the null hypothesis. In this case, the obtained F-value is 2.36, which is less than the critical value of 3.56 for α=0.05. Therefore, the researcher should fail to reject the null hypothesis because the results do not provide enough evidence to conclude that there is a significant difference in the variances between the groups.

It is important to compare the obtained F-value to the critical value at the same significance level to make a decision. There is no need to conduct additional tests such as a chi-square test or t-test for each pair of means unless there is a specific reason to investigate further.