A soft drink company is introducing a new drink and wishes to evaluate which of three different formulas will be most popular.Five people taste each of the three formulas in a random order and rate each formula's taste on a scale from 1 to 10.The results are given below. Farmula 1 Farmula 2 Farmula 3 Person 1 9 6 4 Person 2 7 8 2 Persan 3 5 6 3 Persan 4 7 5 2 Persan 5 8 7 2 \begin{array} { | c | c | c | c | } & ext { Farmula 1 } & ext { Farmula 2 } & ext { Farmula 3 } \\hline ext { Person 1 } & 9 & 6 & 4 \\hline ext { Person 2 } & 7 & 8 & 2 \\hline ext { Persan 3 } & 5 & 6 & 3 \\hline ext { Persan 4 } & 7 & 5 & 2 \\hline ext { Persan 5 } & 8 & 7 & 2 \\hline\end{array} Person 1 Person 2 Persan 3 Persan 4 Persan 5 Farmula 1 9 7 5 7 8 Farmula 2 6 8 6 5 7 Farmula 3 4 2 3 2 2 Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Question

A soft drink company is introducing a new drink and wishes to evaluate which of three different formulas will be most popular.Five people taste each of the three formulas in a random order and rate each formula's taste on a scale from 1 to 10.The results are given below.    Farmula 1   Farmula 2   Farmula 3   Person 1  9 6 4  Person 2  7 8 2  Persan 3  5 6 3  Persan 4  7 5 2  Persan 5  8 7 2 \begin{array} { | c | c | c | c | }  &  	ext { Farmula 1 }  &  	ext { Farmula 2 }  &  	ext { Farmula 3 } \\hline 	ext { Person 1 }  &  9  &  6  &  4 \\hline 	ext { Person 2 }  &  7  &  8  &  2 \\hline 	ext { Persan 3 }  &  5  &  6  &  3 \\hline 	ext { Persan 4 }  &  7  &  5  &  2 \\hline 	ext { Persan 5 }  &  8  &  7  &  2 \\hline\end{array}  Person 1   Person 2   Persan 3   Persan 4   Persan 5  ​  Farmula 1  9 7 5 7 8 ​  Farmula 2  6 8 6 5 7 ​  Farmula 3  4 2 3 2 2 ​ ​   Conduct a Friedman test at the 0.05 level of significance to determine if there are differences in consumer ratings between the three formulas.

Khalid Bashashy · Accepted Answer

Final Answer : H0: The distributions of ratings are identical for all three formulas. HA: At least two of the distributions differ from one another. T1= 13,T2 = 12,T3 = 5 Test statistic: S = 7.6,P-value = 0.0224 Reject the null hypothesis.There is sufficient evidence to suggest that at least two formulas differ in terms of the distribution of ratings.

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