Question

survey of 99 students found that 23% were in favor of raising tuiton to build a new recreation center. The standard deviation of the sample proportion is 6.6%. How large a sample (to the nearest person) would be required to reduce this standard deviation to 5.8%?

Answer 1

Answer:

Given,

To determine sample size

Let us consider,

sqrt(p * (1 - p)/n) = 0.066

sqrt(p * (1 - p)/99) = 0.066

sqrt(p * (1 - p)) = sqrt(99) * 0.066

p(1 - p) = (sqrt(99) * 0.066)^2

p(1 - p) = 0.431244 -------------->(1)

Take the Standard deviation = 0.058

sqrt(p * (1 - p)/n) = 0.058

Substitute (1) in above equation

sqrt(0.431244/n) = 0.058

sqrt(n) = sqrt(0.431244)/0.058

n = 128.2

n = 128