Questions: The following data represent weights (pounds) of a random sample of professional football players on the following teams. X1 = weights of players for the Dallas Cowboys X2 = weights of players for the Green Bay Packers X3 = weights of players for the Denver Broncos X4 = weights of players for the Miami Dolphins X5 = weights of players for the San Francisco Forty Niners You join a Fantasy Football league and you are wondering if weight is a factor in winning Football games What is the MSwithin?

Solution Steps

The sum of squares between groups is calculated as follows:

$$SS_{between} = \sum_{i=1}^k n_i (\bar{X}_i - \bar{X})^2 = 1713.7647$$

The sum of squares within groups is given by:

$$SS_{within} = \sum_{i=1}^k \sum_{j=1}^{n_i} (X_{ij} - \bar{X}_i)^2 = 21761.4118$$

The mean square between groups is calculated using the degrees of freedom between groups:

$$MS_{between} = \frac{SS_{between}}{df_{between}} = \frac{1713.7647}{4} = 428.4412$$

The mean square within groups is calculated using the degrees of freedom within groups:

$$MS_{within} = \frac{SS_{within}}{df_{within}} = \frac{21761.4118}{80} = 272.0176$$

The $F$-statistic is calculated as follows:

$$F = \frac{MS_{between}}{MS_{within}} = \frac{428.4412}{272.0176} = 1.575$$

The $P$-value is calculated using the $F$-distribution:

$$P = 1 - F(1.575; 4, 80) = 0.189$$

Final Answer