A hunting supply store is interested in knowing whether three different brands of goose decoys are equally effective in attracting geese.Each goose decoy is randomly assigned to five hunters,and the order of each experiment is also randomized.An experiment consists of a hunter using one goose decoy with time as the dependent variable.Calculate MST,MSE and the F-ratio.Can you reject H0 using α = 0.05? The ANOVA table is listed below. Analysis of Variance
Source Sum-of-Squares df Mean-Square F-ratio P-value
CallBrand 8.933
Error 6.800
Total 15.733
A)MST = 4.467; MSE = 0.486; F-Ratio = 9.191; Yes,reject H0 using α = 0.05.
B)MST = 4.467; MSE = 0.523; F-Ratio = 8.541; Yes,reject H0 using α = 0.05.
C)MST = 2.978; MSE = 0.567; F-Ratio = 5.252; No,do not reject H0 using α = 0.05.
D)MST = 4.467; MSE = 0.567; F-Ratio = 7.878; Yes,reject H0 using α = 0.05.
E)MST = 2.978; MSE = 0.486; F-Ratio = 6.128; No,do not reject H0 using α = 0.05.

Question

Quizplus · Accepted Answer

The MST is calculated by dividing the sum of squares for CallBrand by its degrees of freedom, which is (3-1)=2. Thus, MST=8.933/2=4.467. The MSE is calculated by dividing the sum of squares for Error by its degrees of freedom, which is (15-3)=12. Thus, MSE=6.800/12=0.567. The F-ratio is calculated by dividing MST by MSE, which is 4.467/0.567=7.878. The p-value is not given, but since the F-ratio is greater than the critical value for α=0.05 with 2 and 12 degrees of freedom in the numerator and denominator, respectively, we can reject the null hypothesis that the brands of goose decoys are equally effective in attracting geese. Therefore, the best choice is D.

A Hunting Supply Store Is Interested in Knowing Whether Three