Question

A Statistics instructor is trying to figure out the percentage of students that still
listen to ”Nirvana”. The instructor is pretty out of touch, so he doesn’t have a prior percentage of students who listen to ”Nirvana” that he can use. How many students should the Statistics instructor sample if he wants to be within 5.5% of the actual percentage of students who listen to Nirvana, using a 95% confidence level. ( For the z value round it to two decimal places)

Answer 1

Solution,

Given that,

=  1 - = 0.5

margin of error = E = 0.055

At 95% confidence level

= 1 - 95%

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z0.025  = 1.96

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

= (1.96 / 0.055)2 * 0.5 * 0.5

= 317.49

sample size = n = 318