Question

Students at a certain school were​ surveyed, and it was estimated that 19​% of college students abstain from drinking alcohol. To estimate this proportion in your​ school, how large a random sample would you need to estimate it to within 0.08 with probability 0.99​, if before conducting the study​ (a) you are unwilling to predict the proportion value at your school and​ (b) you use the results from the surveyed school as a guideline.

a. n=

b. n=

Answer 1

Solution,

Given that,

a) =  1 - = 0.5

margin of error = E = 0.08

At 99% confidence level

= 1 - 99%

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005  = 2.576

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

= (2.576 / 0.08 )2 * 0.5 * 0.5

= 259.21

sample size = n = 260

b) = 0.19

1 - = 1 - 0.19 = 0.81

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

= (2.576 / 0.08 )2 * 0.19 * 0.81

= 159.56

sample size = n = 160