Question

My boss has tasked me with trying to figure out the proportion of people who preferred the online classes better than in person. She'd like me to be precise and have a margin of error of no more than 2%. She also wants to be 99% confident in her results. I, knowing that a lazy mathematician is the best mathematician, don't want to survey and crunch more numbers than i have to. Using the most conservative hypothesized proportion of .50, how many people would i need to survey AT MINIMUM to do what i'm asked?

options: 4161. 416.1 417 41610

Answer 1

Solution,

Given that,

=  1 - = 0.50

margin of error = E = 0.02

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.58

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

= (2.58 / 0.02 )2 * 0.50 * 0.50

= 4160.25

sample size = n = 4161