A quality control inspector wants to estimate the mean inside diameter of the washers produced by a
certain machine. A preliminary sample indicates that the inside diameters have a standard deviation
of 0.30 millimeters. What sample size does he need to estimate the mean to within an error of E = 0.02
millimeters with 90% confidence?
90% = mean ± 1.645 SEm
SEm = SD/√n
.02 = 1.645 SEm
To determine the required sample size to estimate the mean within a specific error with a given level of confidence, we can use the formula for sample size calculation:
n = (Z * σ / E)^2
Where:
n = required sample size
Z = z-score corresponding to the desired confidence level (90% confidence level corresponds to a z-score of 1.645)
σ = standard deviation of the population (0.30 millimeters)
E = desired margin of error (0.02 millimeters)
Substituting the given values into the formula, we have:
n = (1.645 * 0.30 / 0.02)^2
n = 24.70^2
n ≈ 609
Therefore, the inspector would need a sample size of approximately 609 washers in order to estimate the mean inside diameter to within an error of 0.02 millimeters with 90% confidence.