For the data in the source table, what decision can be made about the hypotheses being tested? $$\begin{array} { | l c | c c | c | }
\hline \text { Source } & \text { SS } & d f & M S & F \
\hline \text { Between-groups } & 12.159 & 3 & 4.053 & \
\hline \text { Subjects } & 6.77 & 5 & 1.354 & \
\hline \text { Within-groups } & 20.4 & 15 & 1.360 & \
\hline \text { Total } & 39.329 & 23 & & \
\hline
\end{array}$$
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? $$\begin{array} { | l c | c c | c | } 
\hline \text { Source } & \text { SS } & d f & M S & F \
\hline \text { Between-groups } & 12.159 & 3 & 4.053 & \
\hline \text { Subjects } & 6.77 & 5 & 1.354 & \
\hline \text { Within-groups } & 20.4 & 15 & 1.360 & \
\hline \text { Total } & 39.329 & 23 & & \
\hline
\end{array}$$
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 not provided, but the decision to reject or fail to reject the null hypothesis is based on whether the calculated F exceeds the critical value from F distribution tables, which is not discussed here. Without the F statistic or a critical value for comparison, we cannot conclude if there is a significant effect of the independent variable; thus, we cannot automatically conclude there are differences (reject) or no differences (fail to reject) based on the information given.

For the Data in the Source Table, What Decision Can