Central Limit Theorem for Proportions:
The distribution of sample proportions will be approximately symmetrical when taking repeated samples from a population. The mean of the sample proportions will be equal to the population proportion, and the standard deviation can be calculated using the formula:
standard deviation = sqrt((population proportion * (1 - population proportion)) / sample size)
Central Limit Theorem for Means:
The distribution of sample means will be approximately symmetrical when taking repeated samples from a population. The mean of the sample means will be equal to the population mean, and the standard deviation can be calculated using the formula:
standard deviation = population standard deviation / sqrt(sample size)
It's important to remember that both theorems require random sampling and a sufficiently large sample size for the approximations to be valid. These theorems are essential in statistics as they allow us to make inferences about a population based on sample data.
