Question

1. In a closely contested school bond election, polling indicates that 60% of voters are in favor of the bond and 40% are against the bond. Suppose a random sample of 200 voters is selected.

1. What percentage of the sample would we expect to favor the bond?
2. Does the Central Limit Theorem apply? Write out CLT’s conditions
3. What is the standard error for this sample proportion?

Answer 1

a) The expected percentage of the sample that we expect out of them who will favor the bond is given as: p = 0.6
Therefore 60% is the expected percentage of the sample that would favor the bond.

b) np = 200*0.6 = 120 > 5 and n(1-p) = 200*0.4 = 80 > 5
np(1-p) = 200*0.6*0.4 = 48 >= 10

Therefore the Central limit theorem assumptions are applicable here.

c) the standard error for sample proportion is computed here as:

Therefore 0.0346 is the required standard error for the sample proportion here.