Find a confidence interval given the mean of a sample, ,

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Xiaodan Leng 5 years, 8 months ago

Created this as a copy of Find a confidence interval given the mean of a sample, , .

Name	Status	Author	Last Modified
Find a confidence interval given the mean of a sample, ,	Ready to use	Newcastle University Mathematics and Statistics	13/06/2023 14:40
Ed's copy of Find a confidence interval given the mean of a sample, ,	draft	Ed Stewart	08/03/2019 01:36
Simon's copy of Find a confidence interval given the mean of a sample, ,	draft	Simon Thomas	05/06/2019 10:34
Find a confidence interval given the mean of a sample, ,	draft	Xiaodan Leng	10/07/2019 22:25

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Question statement

A company {sc[s]} {dothis[s]} $\var{sd[s]}$ {units}.

A random sample of $\var{n}$ {t[s]} gives a mean of $\var{m[s]}$ {units}.

Give any introductory information the student needs.

			Name	Type	Generated Value

sd1	number	34.0587727319
sd2	integer	1160
howwell	list	List of 4 items
n	integer	49
doornot	string	does not
uci	number	748.00
test	integer	1
confl	integer	90
spec	string
var1	string	The process variance
var3	string	The variance of the filling pr
var2	string	process variance
sc2ch	string	bolts
units	string	g
zval	number	1.645
sc1ch	string	instant coffee.
lci	number	732.00
tuci	number	748.003811592
lies	string	lie
mm	list	[ 0, 1 ]
dothis	list	List of 4 items
sc4ch	string	supermarkets
m	list	[ 740, 95, 97, 1600 ]
correct	string	no
aim	integer	750
sc3ch	string	tea.
s	integer	0
tlci	number	731.996188408
t	list	List of 4 items
sc	list	List of 4 items
sd	list	[ 1160, 1440, 480, 136.6 ]

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
if(s=3,sd[s],sqrt(sd[s]))

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `number`

34.0587727319

← Depends on:

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
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Part b) Gap-fill
1. Gap Choose one from a list
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Gap-fill

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

Calculate a $\var{confl}$% confidence interval $(a,b)$ for the population mean:

$a=\;$Gap 0.{units} $b=\;$Gap 1.{units}

Enter both to 2 decimal places.

Advice

We use the z tables to find the confidence interval as we know the population variance.

We now calculate the $\var{confl}$% confidence interval.

Note that $z_{\var{confl}}=\var{zval}$ and the confidence interval is given by:

\[ \var{m[s]} \pm z_{\var{confl}}\sqrt{\frac{\var{sd2}}{\var{n}}}\]

Hence:

Lower value of the confidence interval $=\;\displaystyle \var{m[s]} -\var{zval} \sqrt{\frac{\var{sd2}} {\var{n}}} = \var{lci}${units} to 2 decimal places.

Upper value of the confidence interval $=\;\displaystyle \var{m[s]} +\var{zval} \sqrt{\frac{\var{sd2}} {\var{n}}} = \var{uci}${units} to 2 decimal places.

Since $\var{aim}$ {doornot} {lies} in the confidence interval the answer is {Correct}.

Give a worked solution to the whole question.

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Find a confidence interval given the mean of a sample, ,

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Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

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Generated value: `number`

Parts

Gap-fill

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Error

Find a confidence interval given the mean of a sample, ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`