Question

Bank of America wishes to estimate the proportion of cash withdrawals that exceed $50 at all of their ATM machines. They would like to be within 2% of the true proportion with 99% confidence. They know that the true proportion of cash withdrawals that exceed $50 is no more than 30%. How large a sample size is required?

Answer 1

Solution,

Given that,

= 0.30

1 - = 1 - 0.30 = 0.70

margin of error = E = 0.02

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

sample size = n = (Z / 2 / E )2 * * (1 - )

= (2.576 / 0.02 )2 * 0.30 * 0.70

= 3483.78

sample size = n = 3484