7.1 Sampling Distributions

Question 1

What is a sampling distribution?

Answer 1

The distribution of the values of a statistic from all possible samples of a certain size

Question 2

If asked if a given distribution is a sampling distribution, why can we pretty much always say no?

Answer 2

Because any distribution formed from a simulation won’t include every possible sample. It is just useful as an approximate of the sampling distribution.

Question 3

Ignoring sampling methods (chapter 4) how can we tell if a statistic is unbiased?

Answer 3

A statistic is unbiased if the mean of the sampling distribution is equal to the parameter.

Question 4

How do I tell if a given value is a statistic or a parameter?

Answer 4

If it was observed/calculated based on a sample, then it is a statistic. A parameter is usually just a claim that is assumed to be true of a whole population.

Question 5

If all I have is a dotplot, how can I tell what one dot represents?

Answer 5

Usually you can use the label on the dotplot. If the plot is labeled “sample proportions of…” then one dot is the proportion of [context] from one sample.

Question 6

If all I have is a dotplot of a simulation, how do I know if the statistic is unbiased?

Answer 6

Approximate the center of the dotplot (usually median is easiest) and compare it to a given population parameter. If the center is in the right place, the statistic is unbiased.

Question 7

If all I have is a dotplot, how do I test a claim?

Answer 7

Count the dots equal to the claim or more extreme. Divide by the total number of dots and compare to 5%. If less than 5%, we have good evidence something is going on.

Question 8

What’s the difference between the distribution of a sample and the sampling distribution?

Answer 8

The distribution of a sample is just a display of the data actually collected (like what you did for the bias project). The mean or proportion would change from sample to sample. The mean or proportion of the sampling distribution won’t change from sample to sample because it is based on all possible samples.
Alternatively, each dot on a sampling distribution represents a whole sample, each dot on the distribution of a sample just represents one “person” in the sample.