Assume you want to estimate with the propoportion of student who commute less than 5 miles to work(20) with in 2%, what sample size would you need. Total in survey is 233
To estimate the proportion of students who commute less than 5 miles to work within a 2% margin of error, we need to determine the sample size required.
The formula to calculate the sample size for estimating a proportion is given by:
n = (Z^2 * p * (1-p)) / E^2
Where:
n is the required sample size
Z is the Z-score corresponding to the desired level of confidence (e.g., 95% confidence level corresponds to Z = 1.96)
p is the estimated proportion (can be based on previous data or an educated guess)
E is the desired margin of error (as a proportion)
In this case, since we do not have an estimated proportion, we can assume a conservative estimate of 50%, which results in the largest required sample size. Thus, p = 0.5.
Using the given values, let's calculate the required sample size:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2
n = (3.8416 * 0.25) / 0.0004
n = 0.9604 / 0.0004
n = 2401
Therefore, to estimate the proportion of students who commute less than 5 miles to work within a 2% margin of error, you would need a sample size of at least 2401 students.