Question

A confidence interval was used to estimate the proportion of statistics students who are female. A random sample of 72 statistics students generated the following confidence interval: (.438, .642). Using the information above, what sample size would be necessary if we wanted to estimate the true proportion to within 3% using 99% reliability?

Answer 1

Solution :

confidence interval: (0.438, 0.642).

Point estimate = = (Lower confidence interval + Upper confidence interval ) / 2

Point estimate = = (0.438 + 0.642) / 2

Point estimate = = 0.540

= 1 - = 1 - 0.540 = 0.460

Margin of error = E = 0.03

At 99% confidence level

= 1 - 99%

=1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z_0.005 = 2.576

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

= (2.576 / 0.03)² * 0.540 * 0.460

= 1831.47

sample size = n = 1832