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# Informal Confidence Intervals

 Estimating population parameters from a sample The concept of a confidence interval to make an estimate for the actual population median Review of informal confidence intervals from Level 2 AS 2.9 What influences the width of the confidence interval? Using iNZight to investgate confidence intervals Confidence interval demo (allow macros) Stats Learning Workbook Ex C pg 89 - 91 IAS 3.10 pg 22,23

##### Review of informal confidence intervals

We know each sample varies.
How do we make an estimate for the actual population median? (or mean)
Make a confidence interval
An interval within which we can be reasonably sure the actual population mean (or median) occurs

How sure? Reasonably confident (If we made 100 different samples and 100 confidence intervals then about 95% of the confidence intervals would contain the actual population mean) – see Excel demo (allow macros)

Remember Level 2
Informal confidence interval

This is an approximation for the confidence interval

To have a reasonably representative sample we needed a sample size of at least 30 (at level 2)

What if our sample size is smaller?

##### The width of the confidence interval depends of three things

1) The level of confidence. We will be working with about a 95% confidence intervals but we can have different levels of confidence. To be more sure of our estimate of the population parameter the confidence interval would have to be wider.

2) The spread of the population and sample. If the IQR is large then the confidence interval will be wider

3) The sample size. If our sample size is larger then it is more representative of the population, and so our confidence interval will be narrower.

Note the

To halve the confidence interval we need to take a sample 4x as large

What of we can only take a small sample size?

Eg sampling % fat content of pies, or brain weight of dogs

We can use the Bootstrapping re-sampling method to generate a confidence interval
This involves repeated re-sample from a sample with replacement, and repeated many times to form a distribution. This is used to make the confidence interval

###### Using iNZight

Run Confidence interval coverage

Import data

eg male weights popn

This is the population dot plot & box plot & mean

Analyse

Change sample size record results

Include confidence interval history repititions, go

## n=20

What do we notice about the Confidence Interval History?

What does this tell us?

## n=100

What is the effect of changing the sample size?