Question

29. Jason would like to estimate the true proportion of flips a Canadian quarter lands on tails. How many times would Jason have to lip the Canadian quarter to estimate the true proportion of tails to within 0.04 with 90% confidence? (A) 42 (B) 81 (C) 423 (D) 562 (E) 1692

Answer 1

Solution:- (C) The number of times Jason have to flip the Canadian quarter to estimate the true proportion of tails to within 0.04 with 90% confidence is 423.

p = 0.50

M.E = 0.04, C.L = 90%

$M.E = z_{\alpha /2}\times\sqrt{ \frac{p(1-p)}{n}}$

$n =\left ( \frac{z_{\alpha /2}}{M.E} \right )^{2}\times p(1-p)$

$n =\left ( \frac{1.645}{0.04} \right )^{2}\times 0.50(1-0.50)$

n = 422.82

n = 423