Final answer:
The question addresses how to calculate the minimum sample size needed to estimate a population mean, involving concepts such as standard deviation, confidence intervals, and central limit theorem. For accurate estimation using a small sample, a normal population distribution or larger samples are necessary to apply the theorem effectively.
Step-by-step explanation:
The question is asking about determining the minimum sample size required for estimating the population mean μ. To calculate this, we need to know the desired margin of error, the level of confidence we wish to have in our estimate, and the population standard deviation (if known) or some estimate of it.
In situations where the population distribution is not known and the sample size is small (less than 30), we typically rely on the central limit theorem to assume that the sampling distribution of the mean will be approximately normal, provided the sample is randomly selected and that the sample data do not show strong skewness or outliers.
In the example of c), with only four women between the ages of 18-24, the central limit theorem could not be used to assume normality because the sample size is too small.
For the population mean estimation to be accurate, a larger sample size would be needed. When the original population is far from normal, a sample size of at least 30 is recommended or more if there is a significant deviation from normality.
However, if the population standard deviation is known, the EBM formula can help in calculating the required sample size.