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. Find the critical value. $$\begin{array} { l | r | r | r | c | c }
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 30 & 10.00 & 1.6 & 0.264 \
\hline \text { Error } & 8 & 50 & 6.25 & & \
\hline \text { Total } & 11 & 80 & & &
\end{array}$$
A) 1.6
B) 4.07
C) 8.85
D) 7.59

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. Find the critical value. $$\begin{array} { l | r | r | r | c | c } 
\text { Source } & \boldsymbol { D F } & \boldsymbol { S S } & \boldsymbol { M S } & \boldsymbol { F } & \boldsymbol { p } \
\hline \text { Factor } & 3 & 30 & 10.00 & 1.6 & 0.264 \
\hline \text { Error } & 8 & 50 & 6.25 & & \
\hline \text { Total } & 11 & 80 & & &
\end{array}$$
A) 1.6
B) 4.07
C) 8.85
D) 7.59

Quizplus · Accepted Answer

The critical value is the F-statistic with (df factor, df error) degrees of freedom at the chosen level of significance. In this case, df factor = 3 and df error = 8, and the chosen level of significance is 0.05. Using a table of F-distributions or a calculator, we can find that the critical value is approximately 4.07. Since the F-statistic from the ANOVA table (1.6) is less than the critical value, we fail to reject the null hypothesis that the different samples come from populations with the same mean.

Given Below Are the Analysis of Variance Results from a Minitab