
# 5: Estimating Proportions


• 5.1: The Central Limit Theorem for Sample Means (Averages)
In a population whose distribution may be known or unknown, if the size (n) of samples is sufficiently large, the distribution of the sample means will be approximately normal. The mean of the sample means will equal the population mean. The standard deviation of the distribution of the sample means, called the standard error of the mean, is equal to the population standard deviation divided by the square root of the sample size (n).
• 5.2: Using the Central Limit Theorem
The central limit theorem can be used to illustrate the law of large numbers. The law of large numbers states that the larger the sample size you take from a population, the closer the sample mean <x> gets to μ . The central limit theorem illustrates the law of large numbers.
• 5.3: A Population Proportion
The procedure to find the confidence interval, the sample size, the error bound, and the confidence level for a proportion is similar to that for the population mean, but the formulas are different.
• 5.4: A Single Population Mean using the Normal Distribution
A confidence interval for a population mean with a known standard deviation is based on the fact that the sample means follow an approximately normal distribution.