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Estimating population parameters from a sample The concept of a confidence interval to make an estimate for the actual population median What influences the width of the confidence interval? Using iNZight to investgate confidence intervals

Class notes, Class notes Confidence interval demo (allow macros) Stats Learning Workbook Ex C pg 89  91

Review of 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 (at level 2)


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 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 resampling method to generate a confidence interval 

Using iNZight 

Run Confidence interval coverage


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 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? 