Question

1
Select the correct answer.
In a survey conducted with 600 participants across the United States, 450 were found to have studied science in college. If we were to predict the population proportion with a 99.7% confidence, what would the confidence interval be?

A.
69.7% to 80.3%

B.
73.23% to 76.76%

C.
71.46% to 78.53%

D.
73.5% to 76.5%

Answer 1

p̂ = 450/600 = 0.75.
SE = sqrt(p̂(1−p̂)/n) = sqrt(0.75·0.25/600) ≈ 0.01768.
For 99.7% confidence use z ≈ 3, margin = 3·0.01768 ≈ 0.05303.

CI = 0.75 ± 0.05303 = (0.69697, 0.80303) ≈ 69.7% to 80.3%.

Answer: A.