During one of the first \"beer wars\" in the early 1980s. a taste test between S

Question

During one of the first "beer wars" in the early 1980s. a taste test between Schlitz and Budweiser was the focus of a nationally broadcast TV commercial. One hun­dred people agreed to drink from two unmarked mugs and indicate which of the two beers they liked better; fifty-four said, "Bud." Construct and interpret the corresponding 95% confidence interval for p, the true proportion of beer drinkers who preferred Budweiser to Schlitz. How would Budweiser and Schlitz executives each have put these results in the best possible light for their respective companies?

Explanation / Answer

here dample size n=100

proportion Bud liker=p=54/100=0.54

SE(p)=sqrt(p(1-p)/n)=sqrt(0.54*(1-0.54)/100)=0.0498

(1-alpha)*100% confidence interval for p=p±z(alpha/2)*SE(p)

95% confidence interval for sample mean=0.54±z(0.05/2)*0.0498

=0.54±1.96*0.0498=0.54±0.0976=(0.4424,0.6376)

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