Question

Select the correct answer from each drop-down menu.
In a random sample of 75 individuals, 52 people said they prefer coffee to tea.
There is a 99.7% chance that the population mean is between
% and
%. (Choose the option closest to your answer.)

Answer 1

p̂ = 52/75 = 0.6933.
SE = sqrt[p̂(1−p̂)/n] = sqrt(0.6933·0.3067/75) ≈ 0.05317.
99.7% interval ≈ p̂ ± 3·SE = 0.6933 ± 0.1595 → [0.5338, 0.8528].

Approximately 53.4% and 85.3%.