Question

Write a paragraph or more to explain what sampling variability and sampling distribution are, and what they are for?

Answer 1

Ans: Suppose that we draw all possible samples of size n from a given population. Suppose further that we compute a statistic(e.g., a mean, proportion, standard deviation) for each sample. The probability distribution of this statistic is called a sampling distribution. And the standard deviation of this statistic is called the standard error.

Sampling variability is how much an estimate varies between samples. “Variability” is another name for range; Variability between samples indicates the range of valuesdiffers between samples.

Uses of the sampling distribution and variability:

• Since we often want to draw conclusions about something in a population based on only one sample, understanding how our sample statistics vary from sample to sample, as captured by the standard error, is really useful. It allows us to answer questions such as: what is a plausible range of values for the mean in this population given the mean that I have observed in this particular sample? What is the probability of seeing a difference in means between these two treatment groups as big as I have observed just due to chance? Does my study provide any evidence for changing best practice?