Question

According to the Oxnard College Student Success Committee report in the previous year, we believe that 21% of students struggle in their classes because they don't spend more than 8 hours studying independently outside of a 4-unit class. For this year, you would like to obtain a new sample to estimate the proportiton of all Oxnard students who struggle in their classes because they don't study enough outside of the classrooms. You would like to be 99% confident that your estimate is within 4.5% of the true population proportion. How large of a sample size is required? Do not round mid-calculation.

n =

Answer 1

Solution :

Given that,

= 0.21

1 - = 1 - 0.21 = 0.79

margin of error = E = 0.045

At 99% confidence level

= 1 - 99%

=1 - 0.99 = 0.01

/2 = 0.005

Z/2 = 2.576

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

= (2.576 / 0.045)² * 0.21 * 0.79

= 543.642091

sample size = n = 544