Question

An independent-measures ANOVA is used to evaluate the mean differences for a research study comparing four groups with a separate sample of n = 8 in each group

If the data produce an F-ratio of F = 4.60, which of the following is the correct statistical decision?
a) reject the null hypothesis with a =.05 but not with a =.01
b) reject the null hypothesis with either a =. 05 or a =. 01
c) fail to reject the null hypothesis with either a =.05 or a =. 01
d) There is not enough information to make a statistical decision.

Answer 1

The final answer is: "Without information on degrees of freedom, it's impossible to make a statistical decision. Option (d) 'There is not enough information to make a statistical decision' is applicable."

To determine the correct statistical decision, we compare the obtained F-ratio with the critical F-values for the given degrees of freedom and the chosen significance level (α). In this case, there are four groups, and the degrees of freedom for the numerator and denominator need to be considered.

The decision rule is typically based on comparing the obtained F-ratio with the critical F-value at a certain significance level (α). If the obtained F-ratio is greater than the critical F-value, we reject the null hypothesis.

However, we need the degrees of freedom for both the numerator and denominator to look up the critical F-value in a table.

Without this information, we cannot make a definitive decision. Therefore, the correct answer is: d) There is not enough information to make a statistical decision.