Uncertainty of Sample Estimates

Question 1

What does the uncertainty of sample estimates depend on?

Answer 1

Variability in the wider population

Sample size used to calculate the sample mean

Question 2

Describe the normal distribution

Answer 2

Bell shaped
Defined by:
- Mean
- Variance

Question 3

Describe the t distribution

Answer 3

Similar in shape to normal but indexed by number of observations -1
Shape of distribution changes with sample size

Question 4

What is the standard error?

Answer 4

Standard deviation of a sample distribution

Question 5

What does a small standard error mean?

Answer 5

• Sample mean similar to true mean

- High precision

Question 6

What does a large standard error mean?

Answer 6

• Lots of variability

- Low precision

Question 7

What is a confidence interval?

Answer 7

Range of values for the true mean which we are confident that within the true parameter values lies

Question 8

What is the formula for standard error?

Answer 8

s/sqr(n) where n is the sample size

Question 9

What are we required to know before we create a confidence interval?

Answer 9

• How confident we want to be

- How variable our estimate is

Question 10

When would you use an emperical based confidence interval over the normal version?

Answer 10

• Sample size is small

- Parent population is highly skewed

Question 11

Describe the steps for an emperical based confidence interval

Answer 11

1. Select n values at random and with replacement from our original sample of n values
2. For each sample, calculate the mean
3. Examine the distribution of these sample estimates, and locate the values that define the central 95% of the values in this distribution