Question

consider the following table: step 4 of 8: calculate the f - value. please round your answer to two decimal places.

Explanation:

Step1: Calculate degrees of freedom for error

The total degrees of freedom ($DF_{total}$) is 19 and the degrees of freedom among treatments ($DF_{among}$) is 8. The degrees of freedom for error ($DF_{error}$) is calculated as $DF_{total}-DF_{among}$. So, $DF_{error}=19 - 8=11$.

Step2: Calculate mean - square error (MSE)

The mean - square error (MSE) is given by the formula $MSE=\frac{SS_{error}}{DF_{error}}$. We know that the mean - square among treatments ($MS_{among}$) is 258.2. We need to find the $SS_{error}$. First, note that $SS_{total}=8917.39$. Also, $SS_{total}=SS_{among}+SS_{error}$. We don't know $SS_{among}$ yet, but we know $MS_{among}=\frac{SS_{among}}{DF_{among}}$, so $SS_{among}=MS_{among}\times DF_{among}=258.2\times8 = 2065.6$. Then $SS_{error}=SS_{total}-SS_{among}=8917.39 - 2065.6=6851.79$. And $MSE=\frac{SS_{error}}{DF_{error}}=\frac{6851.79}{11}\approx622.89$ (which is already given in the table).

Step3: Calculate the F - value

The F - value is calculated as $F=\frac{MS_{among}}{MSE}$. We know $MS_{among} = 258.2$ and $MSE = 622.89$. So, $F=\frac{258.2}{622.89}\approx0.41$.

Answer:

0.41