What is the formula to calculate the minimum sample size needed for estimating a population mean?
Finding the Minimum Sample Size given margin of error

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Mathematics
•
11th - 12th Grade
•
Hard
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1.
FLASHCARD QUESTION
Front
Back
n = (Z * σ / E)², where n = sample size, Z = Z-value (from Z-table for confidence level), σ = population standard deviation, E = margin of error.
2.
FLASHCARD QUESTION
Front
What does the Z-value represent in the context of sample size calculation?
Back
The Z-value represents the number of standard deviations a data point is from the mean, corresponding to the desired confidence level (e.g., 1.96 for 95% confidence).
3.
FLASHCARD QUESTION
Front
How does increasing the confidence level affect the required sample size?
Back
Increasing the confidence level increases the Z-value, which in turn increases the required sample size to maintain the same margin of error.
4.
FLASHCARD QUESTION
Front
What is the margin of error in statistical terms?
Back
The margin of error is the range within which the true population parameter is expected to lie, given a certain level of confidence.
5.
FLASHCARD QUESTION
Front
If the standard deviation of a population is known, how does it influence sample size determination?
Back
A larger standard deviation increases the required sample size, as it indicates more variability in the population.
6.
FLASHCARD QUESTION
Front
What is the relationship between sample size and the precision of an estimate?
Back
Larger sample sizes generally lead to more precise estimates of the population parameter, reducing the margin of error.
7.
FLASHCARD QUESTION
Front
Calculate the minimum sample size needed to estimate the mean with a standard deviation of 6 ounces, a margin of error of 3 ounces, and a confidence level of 99%.
Back
n = (2.576 * 6 / 3)² = 27.
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