Sampling Variation And Confidence Intervals

Question 1

The list of people that you can choose or sample from is known as what? Give examples

Answer 1

The sampling frame (e.g. the names from the 2001 census of Nottingham)

Question 2

1. Why are samples means different from the true mean?

2. What causes this?

Answer 2

1. Because different random samples will produce slightly different means compared to the overall true mean
2. sampling error

Question 3

What does the central limits theorem state?

Answer 3

That the sampling distribution of the mean approaches a normal distribution as the sample size increases

Question 4

What gives an indication of how well the sample mean reflects the Unknown population mean?

Answer 4

Standard error

Question 5

What determines the accuracy of the sample mean?

Answer 5

• sample size

- variability of the measurement

Question 6

What type of sample do we take to ensure it is representative of the whole population?

Answer 6

A random sample: every individual in the population has an equal chance of being in the sample

Question 7

What is the formula for calculating standard error of the mean?

Answer 7

Standard error = SD divided by the square root of the sample size (n)

Question 8

How do you interpret standard error values?

Answer 8

A large value will tell us that the sample means can be quite different to each other and therefore a particular sample may not be particularly representative of the population

A small value will tell us the sample means will be fairly similar and therefore our particular sample is likely to be a fair reflection of the population

Question 9

What are the confidence intervals?

Answer 9

They out bounds in how far away the truth might be from your estimate

A 95% confidence interval is a range of values around our estimate which we are reasonably confident (95%) includes the true value

Question 10

How is the 95% confidence interval calculated?

Answer 10

The mean plus/minus 1.96 multiplied by the standard error

The 1.96 comes from the normal distribution and actually represents the number of SDs away from the mean which encompasses 95% of the population

Question 11

What does a small confidence interval mean?

Answer 11

That the mean represents the data well

Question 12

What are the two ways of interpreting confidence intervals?

Answer 12

1. A plausible range of values: I.e. The true mean can realistically lie anywhere within those boundaries
2. In terms of repeated experiments: if the experiment was repeated 100 times then 95 of the confidence intervals calculated would contain the true mean