A beverage comopany uses a machine to automatically fill 1-liter bottles. Assume that the population of volumes is normally distributed. The company wants to estimate the mean volume of water to within 1 ML. Determine the minimum sample size required to construct a 95% confidence interval for the population mean. Assume the population standard deviation is 3 ML.
do that thang
do it
To determine the minimum sample size required to construct a 95% confidence interval, we can use the formula:
n = (z * σ / E)^2
Where:
n = sample size
z = z-score corresponding to the desired confidence level (95% in this case)
σ = population standard deviation
E = maximum error, which is half the desired confidence interval (in this case, 1 ML)
Let's plug in the values given:
z = 1.96 (95% confidence level corresponds to a z-score of 1.96)
σ = 3 ML (population standard deviation)
E = 1 ML (maximum error)
n = (1.96 * 3 / 1)^2
n = 5.76^2
n = 33.1776
Since we can't have a fractional sample size, we need to round up to the nearest whole number. Therefore, the minimum sample size required to construct a 95% confidence interval for the population mean is 34.