An independent research firm conducts a study to compare the taste of four new sports drinks.Five people are randomly assigned to each of the four drinks.Each person tastes the drink and judges it on a scale from one to five.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
Drink 25.200
Error 10.000
Total 35.200
A)MST = 6.300; MSE = 0.588; F-Ratio = 10.714; No,do not reject H0 using α = 0.05.
B)MST = 8.400; MSE = 0.588; F-Ratio = 14.286; Yes,reject H0 using α = 0.05.
C)MST = 8.400; MSE = 0.625; F-Ratio = 13.44; Yes,reject H0 using α = 0.05.
D)MST = 8.400; MSE = 0.526; F-Ratio = 15.970; Yes,reject H0 using α = 0.05.
E)MST = 6.300; MSE = 0.625; F-Ratio = 10.080; No,do not reject H0 using α = 0.05.

Question

Quizplus · Accepted Answer

From the ANOVA table, MST (mean square treatment) = 25.200/3 = 8.400 and MSE (mean square error) = 10.000/12 = 0.833.

The F-ratio is calculated as MST/MSE = 8.400/0.625 = 13.44.

To test the null hypothesis that there is no difference in taste among the four sports drinks, we compare the F-ratio to the critical value from the F-distribution with 3 and 12 degrees of freedom (α = 0.05 level of significance). The critical value is 3.01.

Since the calculated F-ratio of 13.44 is greater than the critical value of 3.01, we reject the null hypothesis and conclude that there is a significant difference in taste among the four sports drinks.

Therefore, the best choice is C, which has the correct values for MST, MSE and F-ratio, and the correct conclusion that the null hypothesis is rejected.

An Independent Research Firm Conducts a Study to Compare the Taste