Nayland College

Nayland College - Mathematics

Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links

NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Informal Confidence Intervals

Inference HOME | Achievement Objectives | Overview | Statistical Cycle
- Write an introduction | Using NZgrapher | Discussing sample statistics
- Box plots | Discussing the boxplot & dotplot | Sampling methods | Sample variability and size
- Informal confidence interval | Comparing two populations - discussion
- Writing a report | Revision

10



Estimating population parameters from a sample

What is an informal confidence interval?

What influences the width of the confidence interval?

Using iNZight to investigate confidence intervals

Worksheet and answers on Discussing Informal Confidence Intervals (link to mathstatsfacilitators website)

Research Class notes, Blank notes

Confidence interval demo (allow macros)

Links to Census at school Animations page
Sample size n = 10 animation
Sample size n = 100 animation
Sample size n = 1000 animation

 

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
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


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

 

 

A DEMONSTRATION Using iNZight (not needed for the assessment)

Run the 'Confidence interval Coverage' module in iNZight

 

Import data

eg male weights popn

Add a Variable

This is the population dot plot & box plot & mean

Analyse

Change sample size record results

 

Include confidence interval history repetitions, 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?
 

 

back to top