Perform z-test for hypothesis given sample mean and population variance

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Simon Thomas 6 years, 2 months ago

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Name	Status	Author	Last Modified
Perform z-test for hypothesis given sample mean and population variance	draft	Simon Thomas	07/02/2019 10:24
Simon's copy of Perform z-test for hypothesis given sample mean and population variance	draft	Simon Thomas	05/06/2019 12:35

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Question statement

{this} {stuff}

{claim} $\var{thismuch}$ {units} and {var} {thisvar}.

{test}

To investigate a sample of $\var{n}$ {things} {resultis} $\var{m}$ {units}.

Perform an appropriate hypothesis test to see if the claim made by the customers is substantiated.

Give any introductory information the student needs.

			Name	Type	Generated Value

claim	string	The vending machine company cl
var	string	the variance of the filling pr
pval	integer	3
evi1	list	List of 4 items
crit	list	[ 1.282, 1.645, 2.326 ]
zval1	number	3.4448028487
things	string	cups is taken
tol	number	0.001
units	string	ml
thismuch	integer	140
pm	list	List of 4 items
correctc	string	There is sufficient evidence a
resultis	string	giving a mean of
thisvar	integer	480
test	string	Customers of the vending machi
zval	number	3.445
fac	string	There is insufficient evidence
confl	integer	99
evi	list	List of 4 items
mm	list	[ 0, 0, 0, 1 ]
dothis	string	reject
m	integer	132
dmm	list	[ 0, 1 ]
n	integer	89
this	string	A vending machine fills cups w
stand	integer	25

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"The vending machine company claims each cup should be filled with "

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: `string`

The vending machine company claims each cup should be filled with

This variable doesn't seem to be used anywhere.

Parts

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

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

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

Advice

Step 1: Null Hypothesis

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

Step 2: Alternative Hypothesis

$\operatorname{H}_1\;: \; \mu \lt\;\var{thismuch}$

We should use the z statistic as the population variance is known.

The test statistic:

\[z =\frac{ |\var{m} -\var{thismuch}|} {\sqrt{\frac{\var{thisvar}}{\var{n}}}} = \var{zval}\]

to 3 decimal places.

{table([['Critical Value',crit[0],crit[1],crit[2]]],['p value','10%','5%','1%'])}

We see that the $p$ value {pm[pval]}.

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

{Correctc}

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Part	Test	Passed?
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Gap-fill		Hasn't run yet
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Perform z-test for hypothesis given sample mean and population variance

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `string`

Parts

Gap-fill

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Error

Perform z-test for hypothesis given sample mean and population variance

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Simon Thomas 6 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`