A horticulturist wants to test the effectiveness of four types of fertilizer on the growth rate of Bermuda grass.Six sections of grass are randomly assigned to each of the four fertilizer types,and the rate of growth for each section is measured.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
Fert 283.966
Error 174.218
Total 458.184
A)MST = 56.793; MSE = 8.711; F-Ratio = 6.520; No,do not reject H0 using α = 0.05.
B)MST = 70.992; MSE = 8.711; F-Ratio = 8.150; Yes,reject H0 using α = 0.05.
C)MST = 56.793; MSE = 8.296; F-Ratio = 6.846; No,do not reject H0 using α = 0.05.
D)MST = 94.655; MSE = 8.711; F-Ratio = 10.866; Yes,reject H0 using α = 0.05.
E)MST = 94.655; MSE = 8.296; F-Ratio = 11.410; Yes,reject H0 using α = 0.05.

Question

Quizplus · Accepted Answer

MST = 283.966/3 = 94.655
MSE = 174.218/(6*4-4) = 8.711
F-Ratio = 10.866
Using α = 0.05, and comparing the F-Ratio to the critical value, we have  F(3, 20) = 2.88. Since the calculated F-Ratio is greater than the critical value, we reject H0, and conclude that there is a significant difference among the growth rates of Bermuda grass treated with different types of fertilizer.

A Horticulturist Wants to Test the Effectiveness of Four Types