Suppose you wish to nd out the answer to the age-old question, Do Americans prefer Coke or

Suppose you wish to find out the answer to the age-old question, “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. Results of your taste test indicate that 53 of 100 individuals prefer Pepsi.

(a) Conduct a hypothesis test (preferably using technology)

H0: p = p0 versus H1: p ≠ p0 for p0 = 0.42, 0.43, 0.44, p , 0.64 at the α = 0.05 level of significance. For which values of p0 do you not reject the null hypothesis? What do each of the values of p0 represent?

(b) Construct a 95% confidence interval for the proportion of individuals who prefer Pepsi.

(c) Suppose you changed the level of significance in conducting the hypothesis test to a = 0.01? What would happen to the range of values of p0 for which the null hypothesis is not rejected? Why does this make sense?