Note: Please do not copy paste from Wikipedia/google. thanks a) What is a sampli

Question

Note: Please do not copy paste from Wikipedia/google. thanks

a) What is a sampling distribution (include an APA citation)?

b) What is the Law of Large Numbers?

3) Describe in your own words (do not directly quote any source) the difference between the distribution of a sample and the sampling distribution. Use an example in which the original population has a binomial distribution. You will probably use concepts from the book or another source, so be sure to cite any concepts that come from such sources (even if you paraphrase).

Explanation / Answer

(a)

A sampling distribution is a probability distribution constructed for a particular statistic, like sample means, by drawing a large number of samples from a pre-defined population and then calculating the statistic value for each sample and plotting these values to make a probability plot.

The plot obtained is known as a sampling disribution.

(b)

According to Law of Large Numbers, in an experiment with events having same probability, such as flipping a coin in which both heads and tails have same probability equal to 0.5, when sufficiently large trials are made, the number of occurrences of these events are equal.

This means that if you toss a head 10000 times, then this law states that chances of getting a head and a tail are equal to 5000 each.

(c)

A sample is a collection of data points taken from a specific population, which is supposed to be representative of that population.

The population has many statistics, like mean, mode, variance, etc. The sample is supposed to adequately represent those statistics.

A sampling distribution is a probability distribution plot obtained for a particular test statistic. For example you take many samples of a fixed size from the population and then plot the sample means. This distibution is a sampling distribution for sample means, also called as standard error of the mean.

Hope this helps !

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