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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 
Informal confidence intervalsWe know each sample varies. 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)
This is an approximation for the confidence interval To have a reasonably representative sample we needed a sample size of at least 30


The width of the confidence interval depends of three things1) 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? 