Question

g Suppose we want to know what proportion p of students in a large university have studied calculus in high school. At least how many students should we include in a sample if we want to estimate p with an error bound of 0.03 (at most) with 95% confidence

Answer 1

1067

Explanation:

Given that:

Error (E) = 0.03

Confidence interval = 95% = 0.95

Sample size (n) = ((Zα/2) / Error)^2 * p(1 - p)

Since no assumption is given ; p = 0.5

α = 0.95

Z(1-α/2) = 1.96

(1.96 / 0.03)^2 * 0.5(1 - 0.5)

(65.333333)^2 * 0.5(0.5)

4268.4444 * 0.25

= 1067.1111

n = 1067