Question

Suppose that prior to conducting a coin-flipping experiment, we suspect that the coin is fair. How many times would we have to flip the coin in order to obtain a 98% confidence interval of width of at most .19 for the probability of flipping a head?

a) 150

b) 149

c) 117

d) 116

e) 152

Answer 1

Solution :

=> Answer :- Option a) 150

Given that width w = 0.19

=> Margin of error E = w/2

= 0.19/2

= 0.095

=> For 98% confidence interval, Z = 2.326

=> p = 0.5, q = 1 - p = 0.5

=> Sample size n > p*q*(Z/E)^2

n > 0.5*0.5*(2.326/0.095)^2

n > 149.8691

=> n = 150 (nearest integer)