Finding the Minimum Sample Size given margin of error

Front

What is the formula to calculate the minimum sample size needed for estimating a population mean?

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.

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).

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.

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.

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.

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.

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.

Front

Calculate the minimum sample size needed to estimate the mean with a standard deviation of 8 ounces, a margin of error of 3 ounces, and a confidence level of 99%.

Back

n = (2.576 * 8 / 3)² = 48.

Front

Calculate the minimum sample size needed to estimate the mean with a standard deviation of 9 ounces, a margin of error of 3 ounces, and a confidence level of 99%.

Back

n = (2.576 * 9 / 3)² = 60.

Front

What is the significance of the standard deviation in the context of sample size calculations?

Back

The standard deviation measures the dispersion of data points in a population, affecting the variability and thus the sample size needed for accurate estimates.