In a recent study of student soda preferences in a California high school, 100 r

Question

In a recent study of student soda preferences in a California high school, 100 randomly selected students were each given $1 to purchase a soda from a vending machine that contained a Cola, a Citrus drink, a sports energy drink, and 2% milk. 31 of the students chose the Cola, 22 chose the Citrus drink, 42 chose the sports energy drink, and 5 chose milk. At the .05 level of significance, test the hypothesis that in the population of students at this school, the proportion preferring each of the four drinks is the same.

Explanation / Answer

null hypothesis: proportion of 4 drink is same

alternate hypothesis: proportion is not same for at least two of them.

for above degree of freedom =4-1=3

and test stat chi square =29.36

for which p value =0.0000

as p value is less then 0.05 level we reject null hypothesis and conclude that proportion is not same for all of 4 drinks.

observed Expected Chi square Probability O E=total*p =(O-E)^2/E cola 1/4 31.00 25.00 1.44 citrus 1/4 22.00 25.00 0.36 sports 1/4 42.00 25.00 11.56 milk 1/4 5.00 25.00 16.00 100 100 29.3600

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