Week 7- What is a Sampling Distribution

Question 1

Parameter

Answer 1

A number which describes some characteristic of a population. The exact value of a parameter is usually not known, because we cannot examine the entire population

Question 2

Statistic

Answer 2

A number which describes some characteristic of a sample. The value of the statistic can be computed directly from the sample, and is often used to estimate the value of an unknown

Question 3

Sampling Variability

Answer 3

The value of a statistic varies in repeated random sampling

Question 4

Sampling Distribution

Answer 4

The distribution of values taken by a statistic for all possible samples
of a given size from the same population. This is not necessarily the same type of distribution as
the population distribution!

Question 5

Unbiased Estimator

Answer 5

A statistic is an unbiased estimator if the mean of its sampling
distribution is equal to the true value of the parameter being estimated.

Question 6

Variability of a Statistic

Answer 6

It is described by the spread of its sampling distribution. Spread is
dependent on the size of the sample: larger samples give smaller spread. Spread does not depend on population size as long as the population is at least 10 times larger than the sample

Question 7

The Central Limit Theorem

Answer 7

The sampling distribution of the mean will always be normally distributed, as long as the sample size is large enough. Regardless of whether the population has a normal, Poisson, binomial, or any other distribution, the sampling distribution of the mean will be normal.