Final answer:
To be 95% confident that the sample estimate is within four percentage points of the population proportion, an additional 560 people should be included in the sample.
Step-by-step explanation:
To determine the number of people that need to be included in the sample to be 95% confident that the sample estimate is within four percentage points of the population proportion, we can use the formula for sample size calculation:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the required sample size
- Z is the Z-score (corresponding to the desired confidence level)
- p is the estimated population proportion
- E is the desired margin of error
In this case, we already have a sample of 40 people and the proportion who agree with the policy is 25/40 = 0.625. We want to be 95% confident and have a margin of error of 0.04. The Z-score for a 95% confidence level is approximately 1.96. By substituting these values into the formula, we can solve for n:
n = (1.96^2 * 0.625 * (1-0.625)) / 0.04^2 = 600
Therefore, to be 95% confident that the sample estimate is within four percentage points of the population proportion, an additional 560 people should be included in the sample.