Question 22You’re going to draw a random sample of professional football players because you want to know what percentage have completed high school. You want to have a margin of error of up to 0.03 at a confidence level of 90%. How big should your sample be?1 pointMinimum 456At least 30Minimum 748Minimum 1068
Question
Question 22You’re going to draw a random sample of professional football players because you want to know what percentage have completed high school. You want to have a margin of error of up to 0.03 at a confidence level of 90%. How big should your sample be?1 pointMinimum 456At least 30Minimum 748Minimum 1068
Solution
To calculate the sample size needed for a given margin of error and confidence level, we can use the formula for the sample size of a proportion:
n = (Z^2 * p * (1-p)) / E^2
where:
- Z is the z-score corresponding to the desired confidence level (for a 90% confidence level, Z is approximately 1.645)
- p is the estimated proportion of the population (if we don't have an estimate, we can use 0.5 to maximize the sample size)
- E is the desired margin of error (in this case, 0.03)
If we plug in these values into the formula, we get:
n = (1.645^2 * 0.5 * 0.5) / 0.03^2 = 751.65
Since we can't have a fraction of a person, we round up to the nearest whole number. So, we need a sample size of at least 752.
So, the closest answer among the options provided is "Minimum 748".
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