IB10
May 2012
Mathematical Studies
The Chi-squared (χ2) test with TI-Nspire
To find out if two sets of data are related or not
How do you do it??
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Set up the null hypothesis, Ho (the data sets are independent)
Set up the alternative hypothesis, H1 (the data sets are not independent)
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What significance level to use?
Put the observed data (frequencies) in a contingency table
Calculate the expected frequencies
 f o  f e 2
2
2
Calculate the  - value using the formula  calc  
fe
Find the degrees of freedom (= (rows – 1)(columns – 1)
Find the critical value in the Information booklet
2
If  calc
< critical value 
Accept the null hypothesis
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2
If  calc
> critical value 
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Do not accept the null hypothesis
Or compare the p-values from the GDC
> significant level (1%, 5% or 10%)  Accept the null hypothesis
p-value < significant level (1%, 5% or 10%)  Do not accept the null hypothesis
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If p-value
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If
(If we accept the null hypothesis at the 1% level we are saying that
we are confident that 99% of the time the null hypothesis is correct)
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Examples to do with your TI-Nspire
P.T.O.
MW 2012
Ex 6.9) Is favourite colour of car and gender independent or related?
Use the 5% - significance level and TI-Nspire to find out.
Use these observed data to find out!
Male
Female
Total
BLACK
51
45
WHITE
22
36
RED
33
22
BLUE
24
27
Total
What is your conclusion?
Ex 6.9a) Is the favourite flower independent of gender?
Use the 5% - significance level
Use the observed data from a survey conducted on 80 people outside a florist shop
Male
Female
Total
ROSE
16
19
CARNATION
10
6
LILY
5
4
FREESIA
8
12
Total
What is your conclusion?
Ex 6.9b) Is the type of book you mostly read dependent of age?
Use the 5% - significance level
Use the observed data from an interview with 300 people.
Age/book type
0 – 25 years
26 – 50 years
51 + years
Total
Fiction
23
54
29
Non-fiction Science fiction
16
41
38
38
43
18
What is your conclusion?
MW 2012
Total
Ex 6.9c) Is there any connection between favourite flavour of cat food and breed of cat?
Use the 5% - significance level
Use the observed data from a test with three different flavours of cat food
Persian
Siamese
Manx
Burmese
Total
Beef
4
5
3
6
Chicken
16
11
9
3
Fish
8
18
4
13
Total
What is your conclusion?
Ex 6.9d) Is the favourite type of film independent of gender among 18-year-old youths?
Use the 5% - significance level
Use the observed data from a survey made with sixty 18-year-old youths
Male
Female
Total
Adventure
10
2
Crime
7
8
Romantic
1
14
Comedy
6
3
Sci-fi
8
1
What is your conclusion?
Homework:
Ch. 6.9 (p. 329 - 339) and
the past examination questions for topic 6
MW 2012
Total
Answers from TI-Nspire
Ex 6.9)
Ex 6.9a)
Ex 6.9b)
MW 2012
Ex 6.9c)
Ex 6.9d)
Make sure you know how to use your calculator to help you perform the
the χ2- test with TI-Nspire
It is such a great help for this very time consuming task, don’t you agree???
Cheers,

MW 2012