Testing an hypothesis about the mean of a group (1).

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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

The Arnott’s biscuit company makes "snack packs" of many of its products, including Tiny Teddy (TT) and Pizza Shapes (PS). These packs are labelled "25 g". Test if TT meet the stated weight content. Sample data are in the table below:

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

Are the packets, on average, the correct weight?

In other words, test the following null hypothesis:

H0: Mean weight is equal to 25 g.

Give any introductory information the student needs.

			Name	Type	Generated Value

mu1	number	28
r1	list	[ 25, 25, 25, 25, 25, 25 ]
sig1	number	2.6
t95	number	2.571
thismany	integer	6
tcalc	number	NaN
tupper	number	NaN
tlower	number	NaN
mdupper	number	25.025
mdlower	number	24.975
stdupper	number	0.025
stdlower	number	-0.025
outcome	integer	1
sed	number	0.000
meanwgt	number	25.000
sdwgt	number	0.000
hypval	integer	25
object		Definition of variable `object` is empty.
objects		Definition of variable `objects` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(22..28#0.5)

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`

→ 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

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:

{meanwgt}

Then the standard deviation (sd) of the sample:

{sdwgt}

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.

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Part	Test	Passed?
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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 (1).

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Taxonomy: mathcentre

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Christian Lawson-Perfect 8 years, 9 months ago

Keith McGuinness 9 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Error

Testing an hypothesis about the mean of a group (1).

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`