Question

Suppose you wish to find out the answer to the questions “Do Americans prefer Coke or Pepsi?” You conduct a blind taste test in which individuals are randomly asked to drink one of the colas first, followed by the other cola, and then asked to disclose which drink they prefer. The results of your taste test indicate that 53 of 100 individuals prefer Pepsi. Conduct a hypothesis test to determine if more than 50% of people prefer Pepsi to coca-cola. Use the ? = 0.05 level of significance.

Answer 1

Solution :

Given that,

= 0.50

1 - = 0.50

n = 100

x = 53

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.53

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.50

Ha: p 0.50

Test statistics

z = ( - ) / *(1-) / n

= ( 0.53 - 0.50) / (0.50*0.50) / 100

= 0.60

P-value = P(Z > z )

= 1 - P(Z < 0.60 )

= 1 - 0.7257

= 0.2743

The p-value is p = 0.2743, and since p = 0.2743 > 0.05, it is concluded that the null hypothesis is fail to rejected.

Conclusion:

It is concluded that the null hypothesis Ho is fail to rejected. Therefore, there is not enough evidence to claim that more than 50% of people prefer Pepsi to coca-cola. at the α = 0.05 significance level.