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

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