week 10 sampling distribution

Question 1

parameters

Answer 1

population mean and SD

Question 2

population

Answer 2

all the scores for a particular variable

Question 3

what is an unbiased estimator of the population mean

Answer 3

sample mean

Question 4

what does the sampling distribution tell us

Answer 4

the degree to which samples from a larger population may vary

Question 5

what’s the first part of the central limit theorem

Answer 5

the mean of all possible sample means will be equal to the population mean

Question 6

central limit theorem

Answer 6

If you take a large enough number of random samples from any population (even if the population distribution is not normal), and calculate the mean of each sample, the distribution of those sample means will:

Look like a normal (bell-shaped) distribution as the sample size gets larger.
Have a mean equal to the population mean.
Have a standard deviation called the standard error, which is smaller than the population’s standard deviation.

Question 7

standard error

Answer 7

the SD of the sampling distribution of the mean

provides a measure of spread of sample means, and how far they fall from the population mean

tells us the amount by which we can be wrong in estimating the population mean from sample mean - tell us about reliability

Question 8

standard error gets smaller as….

Answer 8

sample size increases - less chance of one extreme score inflating values

Question 9

summarise standard error and standard deviation

Answer 9

Standard Deviation – measure of the amount that any single score in our sample is different from the mean.
Standard Error – measure of the amount that the sample mean is different from the population mean.

Question 10

standard error is dependent on

Answer 10

sample size

Question 11

what is part 3 of central limit theorem

Answer 11

the sampling distribution of the mean will approach the normal distribution as the sample size (n) increases, regardless of the shape of the original population distribution

Question 12

sum up the Central limit theorem

Answer 12

1. First it specifies that the distribution of sample means will have a mean equal to the value of population mean, mu.
2. Second the distribution of means will have a standard deviation equal to the standard error, σ/√N.
3. Third, as samples gets larger (large is usually defined as 30 or more, bit in some cases it will be much more) the distribution of sample means will become normal.