A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers.A random sample of 25 subscribers to each of the three service providers was taken,and the annual household income for each subscriber was recorded.The partially completed ANOVA table for the analysis is shown here: Complete the ANOVA table by filling in the missing sums of squares,the degrees of freedom for each source,the mean square,and the calculated F-test statistic.
A)Between Groups df = 2,Within Groups df = 74,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 16.79
B)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 16.79.
C)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 9.73
D)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 87,813,791,

Question

A start-up cell phone applications company is interested in determining whether house-hold incomes are different for subscribers to three different service providers.A random sample of 25 subscribers to each of the three service providers was taken,and the annual household income for each subscriber was recorded.The partially completed ANOVA table for the analysis is shown here:  Complete the ANOVA table by filling in the missing sums of squares,the degrees of freedom for each source,the mean square,and the calculated F-test statistic.
A)Between Groups df = 2,Within Groups df = 74,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 16.79 
B)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 16.79. 
C)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 1,474,542,579, MSW = 87,813,791,F = 9.73 
D)Between Groups df = 2,Within Groups df = 72,SSW = 6,322,592,933,MSB = 87,813,791,

Quizplus · Accepted Answer

The ANOVA table shows that there are three groups (service providers) being compared, so the between groups degrees of freedom is equal to the number of groups minus 1, which is 2. The within groups degrees of freedom is equal to the total number of observations minus the number of groups, which is 75-3=72. The sum of squares within groups (SSW) is already given. The total sum of squares (SST) is equal to the sum of squares between groups (SSB) plus the sum of squares within groups, which is SST=SSB+SSW. 
The degrees of freedom for the total sum of squares is equal to the total number of observations minus 1, which is 75-1=74. Therefore, the degrees of freedom for the sum of squares between groups is 74-72=2. 
The mean square for the between groups (MSB) is equal to SSB/df between groups, which is (SST-SSW)/2. The mean square for the within groups (MSW) is equal to SSW/df within groups, which is 6,322,592,933/72=87,813,791. 
Finally, the F-test statistic is equal to MSB/MSW, which is (SST-SSW)/2MSW = 1,474,542,579/87,813,791 = 16.79. Therefore, the best choice is B.

A Start-Up Cell Phone Applications Company Is Interested in Determining