Question

1. Do you find it intuitive, or not, that the mean and standard deviation of a sampling distribution aren't impacted by population size? Explain to a friend who hasn't taken statistics what a sampling distribution is, and what makes them useful. What questions can they help us answer, and what information is required?

Answer 1

Sampling Distribution: "A sampling distribution is a probability distribution of a statistic obtained from a larger number of samples drawn from a specific population. The sampling distribution of a given population is the distribution of frequencies of a range of different outcomes that could possibly occur for a statistic of a population."

Population: "A population is the entire pool from which a statistical sample is drawn. A population may refer to an entire group of people, objects, events, hospital visits, or measurements. A population can thus be said to be an aggregate observation of subjects grouped together by a common feature."

Each sample has its own sample mean and the distribution of the sample means is known as the sample distribution. And this mean may or may not be different from the population mean.

• HOW SAMPLING DISTRIBUTION IS USEFUL

"Sampling distributions are important for inferential statistics. In practice, one will collect sample data and, from these data, estimate parameters of the population distribution. Thus, knowledge of the sampling distribution can be very useful in making inferences about the overall population."

e.g., Knowing the degree to which means from different samples differ from each other and from the population mean would give you a sense of how close your particular sample mean is likely to be to the population mean. Fortunately, this information is directly available from a sampling distribution.

• WHAT ANSWERS THEY CAN HELP US IN FINDING?

Sampling distribution can help us in finding the average height of students of a college by taking random samples of students from random classes, we can find the average per capita income of the city, we can also estimate how much a family spent in the particular city or society by taking random samples , stratified samples, or cluster sampling.

While using sampling distribution following informationa re required :

• · Objective of study
• · Correct proportion of the samples for better inferences
• · Population mean
• · Method of sampling
• · No. of observation in the population.