Question

Why are sampling distributions important to the study of inferential statistics? In your answer, demonstrate your understanding by providing an example of a sampling distribution from an area such as business, sports, medicine, social science, or another area with which you are familiar. Remember to cite your resources and use your own words in your explanation.

Answer 1

Answer:

• sampling distributions important to the study of inferential statistics
• Sampling distributions are an important part of study for a variety of reasons. In most cases, the feasibility of an experiment dictates the sample size.
• Sampling distribution is the probability distribution of a sample of a population instead of the entire population.In simpler words, suppose from a given population you take all possible samples of size n and compute a statistic (say mean) of all these samples.
• If you then prepare a probability distribution of this statistic, you will get a sampling distribution.
• The properties of sampling distribution can vary depending on how small the sample is as compared to the population
• The population is assumed to be normally distributed as is generally the case. If the sample size is large enough, the sampling distribution will also be nearly normal.
• If this is the case, then the sampling distribution can be totally determined by two values - the mean and the standard deviation. These two parameters are important to compute for the sampling distribution if we are given the normal distribution of the entire population.
• standard deviation of the mean is obtained by taking the statistic under study of the sample to be the mean. The say to compute this is to take all possible samples of sizes n from the population of size N and then plot the probability distribution.
• It can be shown that the mean of the sampling distribution is in fact the mean of the population.
• The standard deviation however is different for the sampling distribution as compared to the population. If the population is large enough, this is given by:
• Sampling Distribution Formula:σ_z = σ/√n