Asked by Robert Schofield on May 11, 2024
Verified
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.
Independent Research Firm
An organization that conducts studies and analysis without affiliation to any parties that may influence the outcomes.
Sports Drinks
Drinks formulated to assist sportspeople in rehydrating, along with restoring electrolytes, sugar, and various nutrients, amid or following exercise.
ANOVA
Analysis of Variance, a statistical method used to assess whether there are significant differences between the means of three or more groups.
- Build proficiency in decoding the findings of ANOVA, notably the F-ratio and P-value, for educated hypothesis testing decisions.
- Master the computation of Mean Square Between (MST) and Mean Square Error (MSE) by leveraging Sum-of-Squares and degrees of freedom.
Verified Answer
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.
Learning Objectives
- Build proficiency in decoding the findings of ANOVA, notably the F-ratio and P-value, for educated hypothesis testing decisions.
- Master the computation of Mean Square Between (MST) and Mean Square Error (MSE) by leveraging Sum-of-Squares and degrees of freedom.
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