Ed's copy of Find a confidence interval given the mean of a sample, ,

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Ed Stewart 6 years 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	41.4728827067
sd2	integer	1720
howwell	list	List of 4 items
n	integer	65
doornot	string
uci	number	106.08
test	integer	0
confl	integer	95
spec	string
var1	string	The variance of the filling pr
var3	string	The variance of the filling pr
var2	string	population variance
sc2ch	string	screws
units	string	mm
zval	number	1.96
sc1ch	string	flour.
lci	number	85.92
tuci	number	106.0823928784
lies	string	lies
mm	list	[ 1, 0 ]
dothis	list	List of 4 items
sc4ch	string	supermarkets
m	list	[ 740, 96, 96, 2300 ]
correct	string	yes
aim	integer	100
sc3ch	string	hot water.
s	integer	1
tlci	number	85.9176071216
t	list	List of 4 items
sc	list	List of 4 items
sd	list	[ 1240, 1720, 460, 147.9 ]

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`

41.4728827067

← Depends on:

→ Used by:

tlci
tuci

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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Ed's copy of Find a confidence interval given the mean of a sample, ,

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Ed Stewart 6 years ago

Error in variable testing condition

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Generated value: `number`

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Ed's copy of Find a confidence interval given the mean of a sample, ,

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Ed Stewart 6 years ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`