Answer: The minimum number of students you need if you want the margin of error to be 5% IS 278.
Explanation:
Cochran’s Sample Size Formula gives the minimum number of students as
Where:
e is the desired level of precision (i.e. the margin of error),
p is the (estimated) proportion of the population which has the attribute in question and q is 1 – p.
The z-value for 95% confidence interval is found to be 1.96 in a Z table.
Assuming that half of the teenagers favor the elimination of a curfew: this gives us maximum variability. So p = 0.5 and q=0.5.
Then
Rounding up,
But considering that 1000 is a small population, we can modify the sample size we calculated above formula by using this equation:
Where s is the adjusted sample size, n is the original sample size we calculated and N is the population size.