Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same
Mean. What can you conclude about the equality of the population means? $$\begin{array} { l | r | c | c | c | c }
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\hline \text { Error } & 16 & 13.925 & 0.870 & & \
\hline \text { Total } & 19 & 27.425 & & &
\end{array}$$
A) Accept the null hypothesis since the P-value is greater than the significance level.
B) Reject the null hypothesis since the P-value is greater than the significance level.
C) Accept the null hypothesis since the P-value is less than the significance level.
D) Reject the null hypothesis since the P-value is less than the significance level.

Question

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same
Mean. What can you conclude about the equality of the population means? $$\begin{array} { l | r | c | c | c | c } 
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\hline \text { Error } & 16 & 13.925 & 0.870 & & \
\hline \text { Total } & 19 & 27.425 & & &
\end{array}$$
A) Accept the null hypothesis since the P-value is greater than the significance level.
B) Reject the null hypothesis since the P-value is greater than the significance level.
C) Accept the null hypothesis since the P-value is less than the significance level.
D) Reject the null hypothesis since the P-value is less than the significance level.

Quizplus · Accepted Answer

The F-statistic is 5.17 with a P-value of 0.011, which is less than the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is sufficient evidence to support the claim that the population means are not all equal.

Given Below Are the Analysis of Variance Results from a Minitab