Question

1. A taste test is conducted between two brands of diet cola, Brand A and Brand B, to determine if there is evidence that more people prefer Brand A. A total of 100 people participate in the taste test.

a. If people prefer Brand A and Brand B equally, what proportion of the taste test participants would we expect to choose Brand A?

b. Define the relevant parameter(s) (that is, describe in words with proper notation) and then state the null and alternative hypothesis for testing whether a majority of people prefer Brand A.

c. Give an example of possible sample results that would provide strong evidence that a majority of people prefer Brand A. Give your results as a number choosing Brand A and a number choosing Brand B.

d. Give an example of possible sample results that would provide no evidence that a majority of people prefer Brand A. Give your results as a number choosing Brand A and a number choosing Brand B.

e. Give an example of possible sample results for which the results would be inconclusive. That is, the sample provides some evidence that Brand A is preferred but the evidence is not strong. Give your results as a number choosing Brand A and a number choosing Brand B.

Answer 1

Que.1

a.

If people prefer Brand A and Brand B equally, proportion of the taste test participants would we expect to choose Brand A is 0.5

b.

PA = Proportion of people who choose Brand A.

PB = Proportion of people who choose Brand B

Hypothesis:

c.

Level of significance = 0.05

Sample size n= 20

Number choosing Brand A = 15

Number choosing Brand B = 5

Test statistic, z= 2.236 and p-value= 0.0127  

Since p-value is less than 0.05, we reject null hypothesis, and conclude that majority of people prefer brand A.

d.

Level of significance = 0.05

Sample size n= 20

Number choosing Brand A = 12

Number choosing Brand B = 8

Test statistic, z= 0.894 and p-value= 0.1855  

Since p-value is greater than 0.05, we accept null hypothesis, and conclude that people prefer both brand equally.