If 35 percent of TV viewers recalled seeing an ad for a Ford Explorer on a particular television program based on a sample of 800 viewers,the 95 percent confidence interval for this study would be between approximately:
A)30 percent and 40 percent
B)32 percent and 38 percent
C)28 percent and 42 percent
D)20 percent and 30 percent

Question

Quizplus · Accepted Answer

The formula to calculate the confidence interval for a proportion is:
CI = p ± z*√(p(1-p)/n)
where CI is the confidence interval, p is the proportion, z is the z-score for the desired confidence level (in this case, 1.96 for 95% confidence), and n is the sample size.
Plugging in the numbers given: 
CI = 0.35 ± 1.96*√(0.35(1-0.35)/800) 
CI = 0.35 ± 0.04
CI = (0.31, 0.39)
So the 95% confidence interval for the proportion of TV viewers who recalled seeing an ad for a Ford Explorer is between approximately 31% and 39%. The closest option is B, which is between 32% and 38%.

If 35 Percent of TV Viewers Recalled Seeing an Ad