Sampling Distribution Of Mean And Proportion. Notice that the simulation mimicked a simple random sample of the population which is a straightforward sampling strategy that helps avoid sampling bias. Depending on the question of interest it might make more sense to use the sample proportion or the sample mean to answer the question. In this section we will present how we can apply the Central Limit Theorem to find the sampling distribution of the sample proportion. The sampling distribution of the mean is normally distributed.
Formulas for the mean and standard deviation of a sampling distribution of sample proportionsView more lessons or practice this subject at httpwwwkhanac. If repeated random samples of a given size n are taken from a population of values for a categorical variable where the proportion in the category of interest is p then the mean of all sample proportions p-hat is the population proportion p. Where P is the population proportion and n is the sample size. The mean of our sampling distribution of our sample proportion is just going to be equal to the mean of our random variable X divided by n. σ p P1-P n. In the same way that we were able to find a sampling distribution for the sample mean we can find a sampling distribution for the sample proportion.
So the mean of the sampling distribution of the proportion is μ p 01.
When we found the sampling distribution of the sample mean we did that for a population with continuous probability distribution where the population has a population mean mu. So the mean of the sampling distribution of the proportion is μ p 01. P 1 p n. In this section we will present how we can apply the Central Limit Theorem to find the sampling distribution of the sample proportion. Mean and standard deviation of sample proportions. The sampling distribution of the sample proportion is approximately Normal with Mean μ 043 Standard deviation p 1 p n 043 1 043 75 005717.