Testing an hypothesis about the mean of a group (2).

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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 Testing an hypothesis about the mean of a group (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

As part of regular maintenance, an assistant in an aquarium shop measures the salinity in its sea water tanks every week day (i.e. Monday to Friday). Normal salinity for sea water is 35 ppt (parts per thousand or 35 g of salt in 1 l of water). Sample data are in the table below:

{object}	A	B	C	D	E	F
Weight (g)	$\var{r1[0]}$	$\var{r1[1]}$	$\var{r1[2]}$	$\var{r1[3]}$	$\var{r1[4]}$	$\var{r1[5]}$

Is the salinity normal?

In other words, test the following null hypothesis:

H0: Mean salinity is equal to 35 ppt.

Give any introductory information the student needs.

			Name	Type	Generated Value

hypval	integer	35
mdlower	number	38.358333
mdupper	number	38.408333
meansal	number	38.383333
mu1	number	37.5
object	string	Sample
objects	string	samples
outcome	integer	1
r1	list	List of 6 items
sdsal	number	2.476624
sed	number	1.011078
sig1	number	3.6
stdlower	number	2.451624
stdupper	number	2.501624
t95	number	2.571
tcalc	number	3.346265
thismany	integer	6
tlower	number	3.321265
tupper	number	3.371265

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
35

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`

→ Used by:

tcalc

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

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 sample.

Mean = Gap 0. (input to 2 decimal places )

Standard deviation = Gap 1. (input to 2 decimal places)

Now find the one sample (or "mean to hypothetical value") t-test statistic using the values you have just calculated =Gap 2. (input 2 decimal places)

Is the null hypothesis rejected? Gap 3. Enter 0 for "No" and 1 for "Yes".

Advice

First, recognise that this is a one-sample (or "mean to hypothetical value") t-test.

So calculate the mean of the sample:

{meansal}

Then the standard deviation (sd) of the sample:

{sdsal}

Note: You should use your calculator to get both the mean and standard deviation.

The standard error (se) is calculated as:

\[ se = \frac{ sd }{ \sqrt{ n }} \]

It is:

{sed}

Finally, calculate the test statisitic, t-calc, as the mean difference divided by the standard error:

\[ t-calc = \frac{ mean difference }{ se} \]

t-calc = {tcalc}

There are 6 {objects}, so 5 degrees of freedom, and the test is two-tailed, so the t-table = 2.571.

If t-calc is greater than 2.571, the null is rejected. As this is a two-tailed test, the sign of t-calc (positive or negative) is ignored.

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:

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
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

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Testing an hypothesis about the mean of a group (2).

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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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: `integer`

Parts

Gap-fill

Loading...

Error

Testing an hypothesis about the mean of a group (2).

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: integer

Parts

Gap-fill

Generated value: `integer`