A researcher wishes to estimate the mean height of women aged between 60 and 65 in the US. She desires a margin of error of 0.2 inches. Past studies suggest that a population standard deviation deviation of 3.2 inches is reasonable. Estimate the minimum sample size needed to estimate the population mean with the stated accuracy.
To estimate the minimum sample size needed to estimate the population mean with the desired accuracy, we can use the formula for sample size calculation:
n = (Z * σ / E)^2
Where:
n = sample size
Z = Z-score corresponding to the desired level of confidence
σ = population standard deviation
E = desired margin of error
In this case, the researcher desires a margin of error of 0.2 inches, which means E = 0.2 inches. The past studies suggest a population standard deviation of 3.2 inches, so σ = 3.2 inches.
To determine the Z-score corresponding to the desired level of confidence, we need to specify the level of confidence. Let's assume a 95% confidence level, which corresponds to a Z-score of approximately 1.96.
Plugging in the values into the formula:
n = (1.96 * 3.2 / 0.2)^2
n = (6.272 / 0.2)^2
Calculating the value inside the parentheses:
n = 31.36^2
n ≈ 982.9696
Therefore, the minimum sample size needed to estimate the mean height of women aged between 60 and 65 in the US with a margin of error of 0.2 inches is approximately 983.