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It's believed that as many as 22​% of adults over 50 never graduated from high school. We wish to see if this percentage is the same among the 25 to 30 age group. What sample size would allow us to increase our confidence level to​ 95% while reducing the margin of error to only 5​%?

User AlexBerd
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Answer:

To calculate the sample size required to estimate the percentage of adults over 25-30 who never graduated from high school with a 95% confidence level and a 5% margin of error, we can use the following formula:

n = (Z^2 * p * (1-p)) / E^2

Where:

- n is the sample size

- Z is the z-score associated with the desired confidence level (1.96 for 95% confidence)

- p is the estimated proportion of the population with the characteristic we are interested in (we'll use 0.22, the proportion for adults over 50 who never graduated from high school)

- E is the desired margin of error (0.05)

Plugging in the values, we get:

n = (1.96^2 * 0.22 * (1-0.22)) / 0.05^2

n = 422.5

Rounding up to the nearest whole number, we need a sample size of 423 to estimate the percentage of adults over 25-30 who never graduated from high school with a 95% confidence level and a 5% margin of error.

User IdemeNaHavaj
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