7. Sampling Distributions

Question 1

Why do we have sampling distributions?

Answer 1

A sampling distribution is the distribution of results if all possible samples were selected. The single result obtained in practice is just one of the results in the sampling distribution

Question 2

What is the sampling distribution of the mean?

Answer 2

The sampling distribution of the mean is the distribution of all possible sample means if you select all possible samples of a given size

Question 3

What’s the standard error of the mean?

Answer 3

• Different samples of the same size (n) from the same population will yield different sample means
• A measure of variability in the mean from sample to sample is given by the standard error of the means
• This assumes that sampling is either with replacement, or without replacement from an infinite population

Question 4

Do sampling distributions for the mean have their own formula for z scores?

Answer 4

yes. (xbar-mu)/ pop st dev /(sqrt n)

the sample mean minus population mean, divided by the population st dev, divided by the square root of the sample size.

Question 5

What do we do when we’re trying to find a sample distribution of a non-normal population?

Answer 5

Must apply the CLT.
This states that as the number of values in a sample gets large enough, the sampling distribution of the mean is approximately normally distributed. This is true, regardless of the shape of the distribution of the individual values in the population.

Question 6

what is the sampling distributions of the proportion?

Answer 6

Where we count the number of outcomes in a group. It’s only a proportion if it can’t meet the 4 assumptions of the binomial distributions

Question 7

For most population distributions, n>30 will give

Answer 7

a sampling distribution for the sample mean that is approximately normality

Question 8

For fairly symmetrical distributions

Answer 8

is enough for approximate normality

Question 9

For normal population distributions,

Answer 9

the sampling distribution of the mean is always exactly normally distributed

Question 10

what is the population proportion symbol?

Answer 10

pi, and p estimaties PI.

Question 11

The sampling distribution of the proportion (Z score) generally allows for

Answer 11

for using the normal approximation to estimate the sampling distribution of the proportion

Question 12

When will the sampling distribution of the proportion approximately follow a normal distribution?

Answer 12

nπ and n(1-π) are at least 5 (>=)

Question 13

when asked to find the probability of a sample having a certain percentage amount of an outcome occurring, what must you do first?

Answer 13

First establish that nπ and n(1-π) are at least 5 (>=).

State thus, the normal distribution can be used to approximate this situation.