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

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Newcastle University Mathematics and Statistics

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Newcastle University Mathematics and Statistics 9 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	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Harry's copy of Perform z-test for hypothesis given sample mean and population variance	draft	Harry Flynn	15/11/2018 09:54
STAT7008 Hypothesis test given sample mean and population variance (vending machine)	draft	Catherine Palmer	03/03/2020 21:59

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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	2.7568097504
things	string	cups is taken
tol	number	0.001
units	string	ml
thismuch	integer	147
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	2.757
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	139
dmm	list	[ 0, 1 ]
n	integer	57
this	string	A vending machine fills cups w
stand	integer	24
stuff		Definition of variable `stuff` is empty.

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.

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Generated value: `string`

The vending machine company claims each cup should be filled with

→ Used by:

Statement

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

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Taxonomy: mathcentre

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `string`

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Gap-fill

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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

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: string

Parts

Gap-fill

Generated value: `string`