Question

The College wanted to estimate the proportion of students that take business mathematics. If the college wanted the estimate to be within 5% of the population proportion, how many students would they need to contact? Assume a 99% level of confidence and that the college estimated that 40% of the students take business mathematics.

Answer 1

Solution:
Given in the question
that the college wanted the estimate to be within 5% of the population proportion that mean
Margin of error = 0.05
P(Student take business mathematics) = 0.40
We need to calculate No. of sample
at the 99% confidence interval so alpha = 0.01 and alpha/2 = 0.005 so Zalpha/2 can be from Z table is 2.576
Zalpha/2 = 2.576
Margin of error can be calculated as
Margin of error = Zalpha/2*sqrt(p*(1-p)/n)
n = ((Zalpha/2)/Margin of error)^2 * (p*(1-p))
n = (2.576/0.05)^2 * (0.40*(1-0.40)) = 637.03 or 637
So there is 637 student need to contact so that college estimate to be within 5% of the population proportion.