Question

Determining Sample Size

You want to estimate the percentage of US statistics students who get grades of B or higher. How many such students must you survey if you want 97% confidence that the sample percentages is off by no more than two percentage points?

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.02

At 97% confidence level

= 1 - 97%

= 1 - 0.97 =0.03

/2 = 0.015

Z/2 = Z_0.015 = 2.17

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

= (2.17 / 0.02)² * 0.5 * 0.5

= 2943.06

sample size = n = 2944