Question

1. Discuss the difference between a sample distribution and a sampling distribution.
2. Provide 2 real world examples of when you may make an inference of a population using a sample.

Answer 1

sampling distribution is the theoretical distribution of statistics which is based on different sample distribution .

lets see a example:

suppose we take two sample from experiment of tossing a coin 100 time independently then after studying of histogram ,mean and standard deviation of data we can conclude that sample distribution is binomial.

now suppose we tossing coin 100 times to take a sample and repeated this experment 10000 times. we calculated mean for each sample then by central limit theorem distrubution of mean will be normal distribution and this will be sampling distribution of sample mean.

Sample Distribution:

The sample is a subset of population, and is the set of values you actually use in your estimation. Let’s think 1000 individual you have selected for your study to know about average height of the residents of India. This sample has some quantity computed from values e.g. mean (x ), Standard deviation (s) , sample proportion etc. This is called sample distribution. The mean and standard deviation are symbolized by Roman characters as they are sample statistics.

Sampling Distribution:

Researchers often use a sample to draw inferences about the population that sample is from. To do that, they make use of a probability distribution that is very important in the world of statistics: the sampling distribution. It is theoretical distribution. The distribution of sample statistics is called sampling distribution.