Hypothesis test (t)

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Catherine Palmer 6 years, 3 months ago

Created this as a copy of Hypothesis test (volume).

Name	Status	Author	Last Modified
Perform t-test for hypothesis given sample mean and standard deviation	draft	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Perform t-test for hypothesis given sample mean and standard deviation	draft	Adam Vellender	22/11/2017 16:00
Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Patrice Behan	16/01/2018 14:41
Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Patrice Behan	16/01/2018 14:41
Patrice's copy of Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Patrice Behan	16/01/2018 14:41
Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Patrice Behan	16/01/2018 14:41
Patrice's copy of Patrice's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Patrice Behan	16/01/2018 14:41
David's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	David Goulding	18/09/2018 16:24
Hypothesis test (volume)	draft	Catherine Palmer	29/02/2020 11:30
Harry's copy of Harry's copy of Perform t-test for hypothesis given sample mean and standard deviation two sided, one sample	draft	Harry Flynn	15/11/2018 09:47
Harry's copy of David's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Harry Flynn	15/11/2018 09:49
Hypothesis test (t)	draft	Catherine Palmer	25/11/2018 23:09
Test istotności dla jednej średniej	Ready to use	Aleksandra Romanowska	08/05/2023 12:27

There are 12 other versions that do you not have access to.

Question statement

A leading manufacturer claims its product contains {thisamount} ml by volume. A sample of {n} items was taken and the mean of the sample was $\bar{x}=\var{m}$ ml and the standard deviation of the sample was $s = \var{stand}$ ml. Is the manufacturers claim justified?

Give any introductory information the student needs.

			Name	Type	Generated Value

pval	integer	0
evi1	list	List of 2 items
zval1	number	3.525504583
stand	number	0.93
tol	number	0.001
fac	string	There is insufficient evidence
evi	list	List of 4 items
dothis	string	reject
correctc	string	There is sufficient evidence a
m	number	38.3
dmm	list	[ 0, 1 ]
n	integer	43
mm	list	[ 1, 0, 0, 0 ]
thisamount	number	37.8
zval	number	3.526

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
switch(zval>1.96,0,1)

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`

← Depends on:

zval

→ Used by:

correctc
dmm
dothis
fac
mm

Advice

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
  Add
Part d) Gap-fill
1. Gap Gap 0. Choose one from a list
  Add
2. Gap Gap 1. Choose one from a list
  Add

Gap-fill

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

Step 1: Null Hypothesis

$\operatorname{H}_0\;: \; \mu=\;$Gap 0.

Step 2: Alternative Hypothesis

$\operatorname{H}_1\;: \; \mu \neq\;$Gap 1.

Advice

Step 1: Null Hypothesis

$\operatorname{H}_0\;: \; \mu=\;\var{thisamount}$

Step 2: Alternative Hypothesis

$\operatorname{H}_1\;: \; \mu \neq\;\var{thisamount}$

We should use the z statistic since the sample size is greater than 30.

The test statistic:

\[z = \frac{\var{m}-\var{thisamount}}{\frac{\var{stand}}{\sqrt{\var{n}}}}=\var{zval}\]

to 3 decimal places.

For a significance level of 5%:

$z_{{\frac{\alpha}{2}}}=1.96$

Hence there is {evi1[pval]} evidence against $\operatorname{H}_0$ and so we {dothis} $\operatorname{H}_0$.

{Correctc}

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
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is not used in any exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Catherine Palmer 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Hypothesis test (t)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Catherine Palmer 6 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`