What are some sampling distributions we often analyze in a statistics course?
• Sampling distribution of the sample mean for SRS’s of size n (Recall the Central Limit Theorem. That’s the main result about these.) • Sampling distribution of the sample proportion for SRS’s of size n (Recall the formula for the mean and standard deviation of p-hat.) • My project also has you look at the sampling distribution of the sample range for an SRS of size 2. The point of this is to illustrate that not all statistics are good estimators of their corresponding parameter. When you sketch this sampling distribution, you see that the center of that sampling distribution (also known as the expected value of the statistic) is nowhere near the parameter value. This shows that the sample range would be a very poor estimator of the population range. • Sampling distribution of the sample count of “successes” in a when we measure values on a 0-1 random variable. You should recognize this as having a binomial distribution. Return to the top.
