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 18 and the degrees of freedom among treatments ($DF_{among}$) is 6. The degrees of freedom for error ($DF_{error}$) is calculated as $DF_{total}-DF_{among}$. So, $DF_{error}=18 - 6=12$.

Step2: Calculate mean - square error (MSE)

The sum - of - squares for error ($SS_{error}$) is found by subtracting the sum - of - squares among treatments ($SS_{among}$) from the total sum - of - squares ($SS_{total}$). $SS_{total}=12825.12$ and $SS_{among}$ can be found from the relationship $MS_{among}=\frac{SS_{among}}{DF_{among}}$. Since $MS_{among} = 884.12$ and $DF_{among}=6$, then $SS_{among}=MS_{among}\times DF_{among}=884.12\times6 = 5304.72$. So, $SS_{error}=SS_{total}-SS_{among}=12825.12 - 5304.72=7520.4$. The mean - square error ($MSE$) is $MSE=\frac{SS_{error}}{DF_{error}}=\frac{7520.4}{12}=626.7$.

Step3: Calculate the F - value

The F - value is calculated as the ratio of the mean - square among treatments ($MS_{among}$) to the mean - square error ($MSE$). Given $MS_{among}=884.12$ and $MSE = 626.7$, then $F=\frac{MS_{among}}{MSE}=\frac{884.12}{626.7}\approx1.41$.

Answer:

1.41