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Question

Suppose we want to estimate the proportion of teenagers (aged 13-18) who are lactose intolerant. If we want to estimate this proportion to within 3% at the 95% confidence level, how many randomly selected teenagers must we survey?

Answer 1

We want to find the sample size for selected teenagers who are lactose intolerant. We need to use the formula n = (z²*p*q) / E².

z = z-critical value = 1.96 (based on the 95% confidence interval)

p = proportion of teenagers who are lactose intolerant

q = proportion of teenagers who are not lactose intolerant

E = margin of error = 0.03 (3%)

p and q are unknown. Since we don't know any prior estimate of p, we can assume p = q = 0.5 (50%).

n = (z²*p*q) / E² = (1.96)²(0.5)(0.5) / (0.03)² = 1,067.11 ≈ 1,068

Therefore, to estimate the proportion of teenagers who are lactose intolerant to within 3% at the 95% confidence level, we must survey 1,068 teenagers.