A sampling distribution is a theoretical concept in statistics that refers to the distribution of a statistic calculated from multiple samples of the same size taken from a larger population. It helps us understand the variability of a statistic and make inferences about the population from which the samples were drawn.
Understanding sampling distributions is important because it allows us to make accurate inferences about a population based on a sample. It also helps us assess the reliability of our results and determine the margin of error in our estimates.
A population distribution refers to the distribution of a variable in the entire population, while a sampling distribution refers to the distribution of a statistic calculated from multiple samples of the same size from the population. The shape of a sampling distribution is usually similar to the population distribution, but it tends to be less spread out.
The shape of a sampling distribution is affected by the sample size and the underlying distribution of the population. As the sample size increases, the sampling distribution becomes more normal. If the population distribution is skewed, the sampling distribution will also be skewed.
In hypothesis testing, we compare the results from a sample to the expected distribution under the null hypothesis. The sampling distribution of a statistic, such as the mean or proportion, can help us determine the probability of obtaining our observed results by chance. If the probability is low, we can reject the null hypothesis and conclude that our results are statistically significant.