Perform chi-squared test for differences in preferences

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Perform chi-squared test for differences in preferences	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Brad's copy of Perform chi-squared test for differences in preferences	draft	Brad Allison	20/06/2019 10:21

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Question statement

Some marketing research studies indicate the "positive impact of store brand penetration on store profitability as measured by market share" (Lal,M.C.(2000). Building Store Loyalty Through Store Brands, Journal of Marketing Research, 37, no. 3, pp281).

The manager of a local supermarket that sells four national brands (A, B, C and D) and one store brand (E) of {this} wants to find out whether or not customers have a preference for a particular brand. Over the course of a {thislong}, the number of customers buying each brand of {this} was noted; the results are shown in the table below:

{table1([['A',{a}],['B',{b}],['C',{c}],['D',{d}],['E',{f}]],['Brand','No. of Customers'],true,false,false,true)}

Test the null hypothesis that, in fact, customers at this supermarket do not have a preference for a particular brand of {this}.

Give any introductory information the student needs.

			Name	Type	Generated Value

pval	integer	3
crit	list	[ 7.78, 9.49, 13.28 ]
n	integer	5
chi	number	13.6
tol	number	0.01
correctc	string	there is evidence to suggest t
dh	list	[ "Retain", "Reject" ]
correcth	string	we reject the null hypothesis.
fac	string	there is no evidence to sugges
e1	rational	363/5
a	integer	81
evi	list	List of 4 items
c	integer	54
b	integer	72
d	integer	62
f	integer	94
mm	list	[ 0, 0, 0, 1 ]
dmm	list	[ 0, 1 ]
thislong	string	week
choices	list	List of 4 items
this	string	pineapple juice
t	integer	363
w	integer	1
v	integer	-1
x	list	List of 5 items

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
switch(chi<crit[0],0,chi<crit[1],1,chi<crit[2],2,3)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

← Depends on:

chi
crit

→ Used by:

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dmm
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Part c) Gap-fill

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Ask the student a question, and give any hints about how they should answer this part.

Step 1: Null hypothesis

$\operatorname{H}_0:\;$ Customers do not have a preference for a particular brand of {this}.

Step 2: Alternative hypothesis

$\operatorname{H}_1:\;$ Customers do have a preference for a particular brand of {this}.

Advice

Step 3

Completing the table we have $E= \var{t}/5=\var{t/5}$ for all brands.

We do the last column calculations for brand A.

$\displaystyle \frac{(O -E) ^ 2}{ E} = \frac{(\var{a} -\var{e1}) ^ 2} {\var{e1}} = \var{x[0]}$

to 2 decimal places.

	$O$	$E$	$\displaystyle \frac{(O-E)^2}{E}$
A	$\var{a}$	$\var{e1}$	$\var{x[0]}$
B	$\var{b}$	$\var{e1}$	$\var{x[1]}$
C	$\var{c}$	$\var{e1}$	$\var{x[2]}$
D	$\var{d}$	$\var{e1}$	$\var{x[3]}$
E	$\var{f}$	$\var{e1}$	$\var{x[4]}$
			$\chi^2=\;\var{chi}$

The test statistic is then:

\[\displaystyle \chi ^ 2 = \sum \frac{(O -E)^2}{E} = \var{x[0]} + \var{x[1]} + \var{x[2]} + \var{x[3]} + \var{x[4]} = \var{chi}\]

Step 4:

The degrees of freedom is given by: $\nu$= no. of categories $- 1 = 5-1=4$

The following are the critical values for $\nu=4$.

{table1([['Critical Value',{crit[0]},{crit[1]},{crit[2]}]],['p-value','10%','5%','1%'],false,false,false,false)}

Looking at this test statistic we see that the p-range {choices[pval]}.

The conclusion we come to is that {correctc} Hence {correcth}

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

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Perform chi-squared test for differences in preferences

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Perform chi-squared test for differences in preferences

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Information only

Generated value: `integer`