Find mean and standard deviation of differences between samples

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Mario Orsi 6 years, 1 month ago

Created this as a copy of Find mean and standard deviation of differences between samples.

Name	Status	Author	Last Modified
Find mean and standard deviation of differences between samples	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Nigel's copy of Find mean and standard deviation of differences between samples, , , ,	draft	Nigel Atkins	01/03/2017 11:56
Find mean and standard deviation of differences between samples, , , ,	draft	Nigel Atkins	01/03/2017 13:15
Mario's copy of Find mean and standard deviation of differences between samples	draft	Mario Orsi	08/03/2019 12:11
Find mean and standard deviation of differences between samples	draft	Mario Orsi	13/03/2019 14:47
Find mean and standard deviation of differences between samples	draft	Xiaodan Leng	10/07/2019 23:03

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Question statement

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

{capitalise(object)}	1	2	3	4	5
First {attempt}	{r1[0]}	{r1[1]}	{r1[2]}	{r1[3]}	{r1[4]}
Second {attempt}	{r2[0]}	{r2[1]}	{r2[2]}	{r2[3]}	{r2[4]}

Give any introductory information the student needs.

			Name	Type	Generated Value

meandiff	number	3.4
performing	string	working at $\var{100}$ watts o
attempt	string	attempt
r1	list	[ 16, 18, 15, 15, 16 ]
objects	string	people
mu2	number	18.8
object	string	person
sig1	number	2
thismany	integer	5
stdiff	number	2.408
sig2	number	1.7
something	string	Oxygen uptake values (mL/kg.mi
r2	list	[ 16, 23, 17, 21, 20 ]
mu1	number	17
d	list	[ 0, 5, 2, 6, 4 ]

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`

3.4

← 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

Gap-fill

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

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

Calculate differences for 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:

{capitalise(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{align}
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{align}

Hence the standard deviation is $\sqrt{V}=\var{stdiff}$ to 3 decimal places.

Give a worked solution to the whole question.

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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

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Find mean and standard deviation of differences between samples

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Taxonomy: mathcentre

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Mario Orsi 6 years, 1 month ago

Error in variable testing condition

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Warning

Generated value: `number`

Parts

Gap-fill

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Error

Find mean and standard deviation of differences between samples

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Mario Orsi 6 years, 1 month ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`