A comparison of the means of two groups (3).

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Christian Lawson-Perfect

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8 years, 9 months ago

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Christian Lawson-Perfect 8 years, 9 months ago

Gave some feedback: Ready to use

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Keith McGuinness 9 years, 8 months ago

Created this as a copy of A comparison of the means of two groups (1)..

Name	Status	Author	Last Modified
Paired t-test after treatment.	Ready to use	Bill Foster	01/06/2016 09:47
Christian's copy of Paired t-test after treatment.	Ready to use	Christian Lawson-Perfect	01/06/2016 10:06
A comparison of the means of two groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Testing an hypothesis about the mean of a group (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
Summary statistics (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (3).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of two groups (4).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of three groups (2).	Ready to use	Keith McGuinness	01/06/2016 09:47
A comparison of the means of four groups (1).	Ready to use	Keith McGuinness	01/06/2016 09:47
Simon's copy of Paired t-test after treatment.	draft	Simon Thomas	05/06/2019 14:44

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Question statement

A medical researcher is testing the effect of an extract of a marine snail (found on the shores around Darwin) on wound healing. The test has 6 rabbits in the control group and 6 different rabbits treated with the snail extract. After two weeks, a “wound index” score was recorded for each animal: a smaller number indicates better healing. The data is in the table below:

{object}	A	B	C	D	E	F
Control	$\var{group1[0]}$	$\var{group1[1]}$	$\var{group1[2]}$	$\var{group1[3]}$	$\var{group1[4]}$	$\var{group1[5]}$
Extract	$\var{group2[0]}$	$\var{group2[1]}$	$\var{group2[2]}$	$\var{group2[3]}$	$\var{group2[4]}$	$\var{group2[5]}$

Is there a difference between the average responses in the control and extract groups?

In other words, test the following null hypothesis:

H0: mean control index = mean extract index.

Give any introductory information the student needs.

			Name	Type	Generated Value

combvar	number	2.35
group1	list	[ 17, 19, 19, 17, 17, 19 ]
group2	list	[ 15, 16, 14, 18, 17, 13 ]
mean1	number	18
mean2	number	15.5
mu1	number	18.8
mu2	number	16.1
object	string	Rabbit
objects	string	rabbits
outcome	integer	1
sec	number	0.8850612032
sig1	number	1.5
sig2	number	2.2
t95	number	2.228
thisn	integer	6
var1	number	1.2
var2	number	3.5
tcalc	number	2.8246634143
df	integer	10
slip	number	0.025

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
(var1*(thisn-1)+var2*(thisn-1))/(2*thisn-2)

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`

2.35

← Depends on:

thisn
var1
var2

→ Used by:

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
7. Gap Gap 6. Number entry
  Add
8. Gap Gap 7. Number entry
  Add
9. Gap Gap 8. Number entry
  Add

Gap-fill

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

Summary statistics

Calculate means and variances for both groups: variance ($s^2$) is just the standard deviation ($s$ or $sd$) squared.

Note: All values, except df and outcome, should be given to 2 decimal places.

Mean 1 = Gap 0.; Mean 2 = Gap 1.

Variance 1 = Gap 2.; Variance 2 = Gap 3.

n1 = 6; n2 = 6

Combined standard error

First, calculate the combined variance:

Combined variance = Gap 4.

Second, calculate the combined standard error:

Combined SE = Gap 5.

t-calc and df

$t=\frac{Mean_1 - Mean_2}{SE_c}$

$df = (n1+n2-2) $

t-calc = Gap 6.

df = Gap 7.

Outcome

Compare t-calc to the table value, t-table, which is 2.228, and reject the null if t-calc > t-table.

Outcome = Gap 8. (Enter 0 if the null is accepted; 1 if it is rejected.)

Advice

Summary statistics

Calculate means and variances for both groups: variance ($s^2$) is just the standard deviation ($s$ or $sd$) squared.

Mean 1 = {mean1}; Mean 2 = {mean2}

Variance 1 = {var1}; Variance 2 = {var2}

n1 = 6; n2 = 6

Combined standard error

First, calculate the combined variance:

Combined variance = {combvar}

Second, calculate the combined standard error:

Combined SE = {sec}

t-calc and df

$t=\frac{Mean_1 - Mean_2}{SE_c}$

$df = (n1+n2-2) $

t-calc = {tcalc}

df = {df}

Outcome

Compare t-calc to the table value, t-table, which is 2.228, and reject the null if t-calc > t-table.

Outcome = {outcome} (Enter 0 if the null is accepted; 1 if it is rejected.)

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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A comparison of the means of two groups (3).

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

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Error

A comparison of the means of two groups (3).

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`