Final answer:
To determine the sample size needed to provide a 95% confidence interval with a margin of error of 7, use the formula: Sample size = (Z^2 * (p * (1-p))) / (E^2). Plugging in the values, the sample size would be approximately 106.
Step-by-step explanation:
To determine the sample size needed to provide a 95% confidence interval with a margin of error of 7, you need to use the formula:
Sample size = (Z^2 * (p * (1-p))) / (E^2)
Where:
- Z: The Z-score corresponding to the desired confidence level. For a 95% confidence level, the Z-score is approximately 1.96.
- p: An estimate of the proportion from the population. Since the proportion is not mentioned in the question, you can assume a conservative estimate of 0.5.
- E: The margin of error, which is 7 in this case.
Plugging in these values into the formula, the sample size would be approximately 106.