Question

The NWBC found that 13% of women-owned businesses provided profit-sharing and/or stock options. What sample size could be 98% confident that the estimated (sample) proportion is within 5 percentage points of the true population proportion?

Answer 1

Solution:

Given that,

= 0.13

1 - = 1 - 0.13 = 0.87

margin of error = E = 5% = 0.05

) At 98% confidence level the z is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z_0.01 = 2.326

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

= (2.326/ 0.05)² * 0.13 * 0.87

= 244.76

= 245

n = sample size = 245