Simon's copy of Pearson1

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Simon Thomas 6 years ago

Created this as a copy of Pearson1.

Name	Status	Author	Last Modified
Pearson1	draft	Bill Foster	06/08/2020 08:41
Pearson1	Ready to use	Julie Crowley	24/01/2025 17:11
Exam vesrion of Pearson1	Ready to use	Julie Crowley	13/11/2020 16:01
Simon's copy of Pearson1	draft	Simon Thomas	27/03/2019 11:32

There are 11 other versions that do you not have access to.

Question statement

It is well known that similarity in attitudes, beliefs and interests plays an important role in interpersonal attraction. A researcher developed a questionnaire which was completed by 8 married couples. One question sought to place each individual on a 20 point scale in which low scores represent liberal attitudes and high scores represent conservative attitudes. The data were:

Couple	$\var{obj[0]}$	$\var{obj[1]}$	$\var{obj[2]}$	$\var{obj[3]}$	$\var{obj[4]}$	$\var{obj[5]}$	$\var{obj[6]}$	$\var{obj[7]}$
Wife $(X)$	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$	$\var{r1[6]}$	$\var{r1[7]}$
Husband $(Y)$	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$	$\var{r2[5]}$	$\var{r2[6]}$	$\var{r2[7]}$

Give any introductory information the student needs.

			Name	Type	Generated Value

tsqovern	list	[ 946.125, 1104.5 ]
obj	list	List of 8 items
r1	list	[ 20, 8, 13, 7, 1, 16, 17, 5 ]
r2	list	List of 8 items
ss	list	[ 306.875, 327.5 ]
m	integer	20
k	integer	3
ssq	list	[ 1253, 1432 ]
n	integer	8
spcoef	number	0.214
corrcoef	number	0.85
vs	list	[ 0, 0, 0, 0, 1 ]
spxy	number	269.75
t	list	[ 87, 94 ]
tol	number	0.01
v	list	[ 0, 1, 0, 0, 0 ]
sxy	number	1292
ssd	number	18
rr2	list	[ 7, 1, 6, 3, 2, 5, 8, 4 ]
rr1	list	[ 8, 4, 5, 3, 1, 6, 7, 2 ]
d	list	[ 1, 3, -1, 0, -1, 1, -1, -2 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
[t[0]^2/n,t[1]^2/n]

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: `list`

[ 946.125, 1104.5 ]

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
4. Gap Gap 3. Number entry
  Add
5. Gap Gap 4. Number entry
  Add
6. Gap Gap 5. Number entry
  Add
1. Step Information only

Gap-fill

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

Wife $(X)$	$\sum x=\;$Gap 0.	$\sum x^2=\;$Gap 1.
Husband $(Y)$	$\sum y=\;$Gap 2.	$\sum y^2=\;$Gap 3.

Also find $\sum xy=\;$Gap 4..

Hence calculate the Pearson correlation coefficient $r$ correct to 2 decimal places:

$r=\;$Gap 5.

Advice

$\sum x = \var{r1[0]}+\var{r1[1]}+\var{r1[2]}+ ... = \var{t[0]}$

$\sum x^2 = \var{r1[0]}^2+\var{r1[1]}^2+\var{r1[2]}^2+ ... = \var{ssq[0]}$

$\sum y = \var{r2[0]}+\var{r2[1]}+\var{r2[2]}+ ... = \var{t[1]}$

$\sum y^2 = \var{r2[0]}^2+\var{r2[1]}^2+\var{r2[2]}^2+ ... = \var{ssq[1]}$

$\sum xy = (\var{r1[0]}\times\var{r2[0]})+(\var{r1[1]}\times\var{r2[1]})+(\var{r1[2]}\times\var{r2[2]})+...=\var{sxy}$

To calculate the Pearson correlation coefficient $r$ we use the formula:

\[r=\frac{n\Sigma xy -\Sigma x \Sigma y}{\sqrt{n\Sigma x^2-(\Sigma x)^2}\sqrt{n\Sigma y^2-(\Sigma y)^2}}\]

Note that $n$ is the number of data points. In this case $n=\var{n}$

Hence

$r=\frac{n\Sigma xy -\Sigma x \Sigma y}{\sqrt{n\Sigma x^2-(\Sigma x)^2}\sqrt{n\Sigma y^2-(\Sigma y)^2}}$

$r=\frac{\var{n}\times\var{sxy} -\var{t[0]}\times\var{t[1]}}{\sqrt{\var{n}\times\var{ssq[0]}-(\var{t[0]})^2}\sqrt{\var{n}\times\var{ssq[1]}-(\var{t[1]})^2}} = \var{corrcoef}$

Give a worked solution to the whole question.

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

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
Number entry
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Information only

This question is used in the following exam:

Correlation and regression by Simon Thomas in Maths support.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Simon Thomas 6 years ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Simon's copy of Pearson1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`