Question

Metro Bank wants to estimate the proportion of cash withdrawals that are greater than $100 at its ATM machine. They want their estimate to be within 1.50% percent of the true population proportion, with 95% confidence. How large a sample is needed to estimate the proportion of cash withdrawals that are greater than $100 at its ATM machine?

Answer:____________

Answer 1

Solution :

Given that,

= 0.5

1 - = 0.5

margin of error = E = 0.0150

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

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

= (1.96 / 0.0150)² * 0.5 * 0.5

= 4268.44

sample size = 4269

Answer: = 4269