For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} {| l |c| c | c c |}
\hline \text { Source } & S S & d f & M S & F \
\hline \text { Between-groups } & 10.1 & 2 &5.05 \
\hline \text { Subjects } & 7.4 & 4 & 1.85 \
\hline \text { Within-groups } & 8.5 & 8 & 1.036 \
\hline \text { Total } & 26 & 14 & \
\hline
\end{array}$$
A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Question

For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} {| l |c| c | c c |} 
\hline \text { Source } & S S & d f & M S & F \
\hline \text { Between-groups } & 10.1 & 2 &5.05 \
\hline \text { Subjects } & 7.4 & 4 & 1.85 \
\hline \text { Within-groups } & 8.5 & 8 & 1.036 \
\hline \text { Total } & 26 & 14 & \
\hline
\end{array}$$
A) Fail to reject the null hypothesis because the F statistic does not exceed the critical cutoff.
B) Fail to reject the null hypothesis and conclude there is no effect of the independent variable.
C) Reject the null hypothesis and conclude there are differences among the levels of the independent variable.
D) Reject the null hypothesis and conclude the independent variable has no effect.

Quizplus · Accepted Answer

The F statistic is calculated as the ratio of the mean square between-groups to the mean square within-groups, which is 5.05 / 1.036 = 4.874. If this F value exceeds the critical value from the F distribution table for the given degrees of freedom, the null hypothesis is rejected, indicating differences among the levels of the independent variable.

For the Data in the Source Table, What Decision Can