Find mean and standard deviation of differences between samples

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Christian Lawson-Perfect

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Paul Finley

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Ready to use

3 years, 8 months ago

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Paul Finley 3 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 10 years ago

Created this as a copy of Descriptives.

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Question statement

{Something} for $\var{thismany}$ {objects} {performing} were:

{object}	1	2	3	4	5
First {attempt}	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$
Second {attempt}	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$

Answer the following questions to 3 d.p.:

Give any introductory information the student needs.

			Name	Type	Generated Value

meandiff	number	3.2
performing	string	working at $\var{100}$ watts o
attempt	string	attempt
r1	list	[ 21, 16, 18, 23, 18 ]
objects	string	people
mu2	number	22.4
object	string	Person
sig1	number	2
thismany	integer	5
stdiff	number	4.324
sig2	number	1.6
something	string	Oxygen uptake values (mL/kg.mi
r2	list	[ 20, 22, 24, 21, 25 ]
mu1	number	19.5
d	list	[ -1, 6, 6, -2, 7 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
mean(d)

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: `number`

3.2

← Depends on:

→ Used by:

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

Gap-fill

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

Find the mean and standard deviations of the difference between first and second {attempt}s.

Calculate differences for second {attempt} – first {attempt}.

Please note that it is second {attempt} – first {attempt}

Mean of difference = Gap 0. (input as an exact decimal)

Standard deviation of difference = Gap 1. (input to 3 decimal places)

Advice

The table of differences is given by:

{object}	1	2	3	4	5
First {attempt}	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$
Second {attempt}	$\var{r2[0]}$	$\var{r2[1]}$	$\var{r2[2]}$	$\var{r2[3]}$	$\var{r2[4]}$
Differences	$\var{d[0]}$	$\var{d[1]}$	$\var{d[2]}$	$\var{d[3]}$	$\var{d[4]}$

The mean of the differences is $\var{meandiff}$.

The variance $V$ of the differences is
\[\begin{eqnarray*} V&=&\frac{1}{4}\left(\simplify[]{({d[0]}^2+{d[1]}^2+{d[2]}^2+{d[3]}^2+{d[4]}^2)}-5\times \var{meandiff}^2\right)\\ &=&\var{variance(d,true)} \end{eqnarray*} \]
Hence we have the standard deviation = $\sqrt{V}=\var{stdiff}$ to 3 decimal places.

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

This question is used in the following exam:

Maths Support: Descriptive statistics by Christian Lawson-Perfect in Maths Support Wiki.

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Find mean and standard deviation of differences between samples

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Paul Finley 3 years, 8 months ago

Christian Lawson-Perfect 10 years ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Find mean and standard deviation of differences between samples

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Paul Finley 3 years, 8 months ago

Christian Lawson-Perfect 10 years ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`