Question

The Bengie Beverage Company is entering the sparkling beverage market and wants to know if beverage drinkers prefer a particular brand. They will use a blind taste test. One hundred and sixty drinkers are offered four different beverages in identical containers. They are asked to pick their favorite. The numbers in parentheses identify the number who chose that beverage. The results are: Beverage A (36); Beverage B (45); Beverage C (50); and Beverage D (29). At the 1% level of significance, are the beverage types equally preferred?

Answer 1

i am denoting beverage A by 1,beverage B by 2, beverage C by 3 , beverage D by 4

hypothesis:-

[ all the four proportions are equal]

at least one of the proportion is not equal

the calculation table be:-

beverage	observed frequency (Oi)	expected frequency (Ei)
A	36	160*0.25 = 40	0.4
B	45	40	0.625
C	50	40	2.5
D	29	40	3.025
total	160		6.55

test statistic be:-

df = (4-1) =3

p value = 0.0877

[ in any blank cell of excel type =CHISQ.DIST.RT(6.55,3) press enter]

decision:-

p value = 0.0877 >0.01 (alpha)

so, we fail to reject the null hypothesis.

conclusion:-

there is sufficient evidence at the 1% level of significance to claim that the beverage types equally preferred.

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