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AS 3.2 Confidence Intervals

Confidence Intervals HOME | Achievement Objectives | Overview | Sample Totals | Central Limit Theorem | Revision

Achievement Standard 3.2 Confidence Intervals is a 3 credit externally assessed topic

Confidence Interval Starters

1

 

 Distribution of the sample total.

Confidence Intervals Overview
What happens when we repeatedly take samples from a population and add to get a total?

What is the distribution of the sample totals taken

 Ex 3.01 page 58 #3,4,5,6

MR notes, Blank Notes

 

Rolling dice simulation of TOTALs

Dice distribution of TOTALs

 pg 30

2

 

 Distribution of the sample mean

What is the distribution produces when repeated samples of size 'n' are taken from a population?
What is the central limit theorem?

MR notes, Blank Notes

Ex 3.02 page 61 #7,8,9,10

Rolling dice simulation of MEANS
Sampling from a normal distribution
Sampling from a flat distribution
Sampling from a 'U' distribution

http://www.btinternet.com

 

3

 

 Parameters for means & totals

Summary of distributions of 'means' and 'totals'
What are the parameters for distribution of sample means compared with sample totals?

MR notes, Blank Notes

 

4

 

 Probabilities for a sample total T

Solve Normal Distribution problems when a sample of size 'n' is added to give a sample total 'T'. 

MR notes, Blank Notes

Ex 3.03 page 64 #3,4,5,6 | #7,8,9

pg 33,

 

5

 

 Probabilities for a sample mean

Solve distribution problems when samples of size 'n' are taken from a population and then averaged to give a sample mean.  

MR notes, Blank Notes

Ex 3.04 page 66 #4,5,6 | #8,9,10,11

pg 31, 32

 

6

 

 Mixed problems

Solving mixed total and mean problems for samples of size 'n' taken from a population.

MR notes, Blank Notes

Ex 3.05 page 68 #3,4,5,6 | #7,8,9

 

 

7

 

 Confidence interval for a mean

Calculate the confidence intervals for sample means.
What does a confidence interval represent?
How do you determine the level of confidence?
What can change the width of the confidence interval?

MR notes, Blank Notes

Finding confidence intervals demo
Excel conf interval demo

pg 35

8

 

 Practising calculating confidence intervals

Confidence Interval Description

 

MR notes, Blank Notes

Ex 4.01 page 75 #1,2,3,5,6 | #10,11,12,13,14

pg 36

9

 

 Calculating sample size 'n'

How do we calculate the sample size required for any given margin of error?
How should the value of 'n' be rounded?

MR notes, Blank Notes

Ex 4.02 page 79 #1,2,3,4,5 | #6,7,8

pg 37

 

10

 

 Confidence intervals for the difference between two means.

If sample values were taken from a population and the difference between the values calculated, what would the resulting distribution?

How do we calculate the confidence interval for the difference between two means? (and impress our friends)

How do we determine if the two populations are significantly different - or not?

MR notes, Blank Notes

Ex 4.03 page 83 #5,6 | #10,11

 

 

Difference between means demo

 pg 40, 41

11

 

 Confidence intervals for a proportion

How do we calculate the Confidence interval for a proportion?

What does this represent?

MR notes , Blank Notes

Ex 5.01 pg 88 #5,6,7 | #8,9,10

 

 pg 34, 38

 

12

 

 Calculating sample size for a proportion 

How do we calculate the required sample size for a confidence interval of a proportion given a certain margin of error and level of confidence?

What is the margin of error for a confidence interval of a proportion? 

Confidence intervals review

Formula Sheet | pdf version

MR notes, Blank Notes | MR notes, Blank Notes

Ex 5.02 page 91 #4,5,6,7 | #8,9,10,11
 Ex 5.03 page 95 #3,4,5 | #6,7,8

 pg 39  

13

 

 Revision

Revision Assignment and solutions

 

Links: POPES 3.2 Revision Sheets

1 2 3 4 5 6 7 8 9 10

 42, 43, 44  

14

 

 Practice assessment AS 3.2 Confidence Intervals    

 

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