Final answer:
To determine the sample size needed for a 95 percent confidence interval with a margin of error less than 0.02 for the true proportion of high school students who attend home basketball games, use the formula and a conservative choice for the sample size.
Step-by-step explanation:
To determine the sample size needed to get a margin of error less than 0.02, we can use the formula for sample size:
n = (Z^2 * p * (1-p)) / E^2
Where:
- n is the sample size
- Z is the z-score corresponding to the desired confidence level
- p is the estimated proportion of the population attending home basketball games
- E is the desired margin of error
Since we have no prior estimate of the proportion, we need to choose a conservative value for p. A conservative estimate for the proportion is 0.5, which maximizes the sample size. For a 95% confidence level, the z-score is approximately 1.96. Plugging these values into the formula, we have:
n = (1.96^2 * 0.5 * (1-0.5)) / 0.02^2
Simplifying the equation, we get:
n ≈ 3841
Therefore, Cora must have a sample size of at least 3841 to get a margin of error less than 0.02.