Sampling Distributions

Question 1

What are sampling distributions?

Answer 1

how sample statistics are themselves distributed when we repeatedly sample from a population

Question 2

What does the sampling distribution of the mean (SDM) describe?

Answer 2

how the sample mean is distributed

Question 3

What is a sampling error and how can it be reduced?

Answer 3

the error associated with examining statistics calculated by a sample rather than the whole population
- reduced by using a larger sample

Question 4

What is the magnitude of sampling error?

Answer 4

how far sample statistics depart from the population parameters

Question 5

What does the magnitude is sampling error depend on?

Answer 5

• sample size
• Bigger sample -> bigger sampling error less likely
• Smaller Sample -> bigger sampling error more likely

Question 6

Why is it more likely for there to be sample errors when sampling small samples?

Answer 6

because it is more likely that you will sample from the same side of the mean

Question 7

How do you obtain sample statistics?

Answer 7

By repeatedly sampling from a population

Question 8

How do you generate a sampling distribution?

Answer 8

1. Take a sample (size N) from a population
2. Calculate a sample statistic
3. Add the new statistic to a frequency plot (a histogram of the sample statistic)
4. Repeat these three steps
   - you can use any sample statistic

Question 9

What valuable information does sampling distributions tells us?

Answer 9

What the mean values of the statistic is over all samples

• how variable the statistic is over all samples
• what shape the distribution is over all samples

Question 10

For a variable that is normal what is the sample distribution of the mean?

Answer 10

• also normal
• mean = u (same as parent population
• standard deviation (sigmaSDM) = sigma (s.d) parent population/ square root of sample size (square root N) (this is the standard error)
• standard error of SDM must be smaller than the standard deviation of the parent population

Question 11

What is the standard error of the mean (s.e.m) and how do you calculate it?

Answer 11

standard deviation of the sampling distribution of the mean (square root N)

• standard deviation of parent population/ square root of sample size
• sigma (parent pop)/ (square root N)

Question 12

Why can you work out the Z score from a sample distribution graph?

Answer 12

Because it is normal

Question 13

What is a sample distribution graph?

Answer 13

distribution of sample mean m for sample size N drawn at random from the parent population above

Question 14

What is the central limit theorem?

Answer 14

• Given a population with a mean u and s.d. sigma, the sampling distribution of the mean approaches a normal distribution with mean u and s.d. sigma/square root N as N, the sample size, increases
• This is true regardless of the underlying distribution
• So even if your population is not normal the distribution of means sample from it will be

Question 15

How do you work out Zm (z score for the SDM)?

Answer 15

• Zm = (m – u)/ sigma (s.d. parent pop)/ square root N

- = (sample mean - mean)/ standard error