# What is a confidence interval?

## Learning outcomes:

On watching this video, students should be able to:

- Explain the behaviour of a confidence interval over repeated independent sampling and how this is linked to the interpretation of a confidence interval as "providing a range of values which we are XX% (typically 95%) confident contain the true population value".
- Explain why the following interpretation of a 95% confidence interval is incorrect "there is a 95% probability that the true population value is lies within this interval"
- Describe a confidence interval in 3 ways: (1) in terms of its long run behaviour from repeated sampling; (2) in terms of a range of plausible values for the population parameter; and (3) in terms of a minimum measure of error or precision, telling us how little our point estimate might tell us about the true value if there is no bias.
- Calculate a 95% confidence interval for a sample mean using the basic formula:

Point estimate ± 1.96*standard error

4. State and explain how sample size and level of confidence affect the width of a confidence interval.

Correction

13:40 The slide should state “………on only 5% of occasions from repeated sampling would we expect not to capture the true value” NOT “………on only 5% of occasions from repeated sampling would we expect not to capture the confidence interval” I also repeat this mistake when I read the slide!