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

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Simon Thomas 5 years, 9 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	21.9089023002
sd2	integer	480
howwell	list	List of 4 items
n	integer	66
doornot	string
uci	number	101.29
test	integer	0
confl	integer	95
spec	string	the timecards of
var1	string	The variance of the filling pr
var3	string	The process variance
var2	string	population variance
sc2ch	string	bolts
units	string	ml
zval	number	1.96
sc1ch	string	sugar.
lci	number	90.71
tuci	number	101.2857269217
lies	string	lies
mm	list	[ 1, 0 ]
dothis	list	List of 4 items
sc4ch	string	fast food outlets
m	list	[ 722, 97, 96, 1200 ]
correct	string	yes
aim	integer	100
sc3ch	string	tea.
s	integer	2
tlci	number	90.7142730783
t	list	List of 4 items
sc	list	List of 4 items
sd	list	[ 1120, 1340, 480, 164.8 ]

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`

21.9089023002

← Depends on:

→ Used by:

tlci
tuci

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

(a)

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

Our confidence interval for the mean is given by $\bar x \pm z^* \frac{\sigma}{\sqrt{n}}$ where $z^*$ is taken from standard normal distribution tables and depends on our confidence level.

Note $\sigma = \sqrt{\sigma^2}=\sqrt{\var{sd2}}$

Thus to calculate the two-sided $\var{confl}$% confidence interval, we note that $z^* = z_{\var{confl}}=\var{zval}$ and so the confidence interval is given by:

\[\bar x \pm z_{\var{confl}} \frac{\sigma}{\sqrt{n}}= \var{m[s]} \pm \var{zval}\frac{\sqrt{\var{sd2}}}{\sqrt{\var{n}}}\]

Hence:

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

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

(b)

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

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This question is used in the following exam:

Confidence Intervals and Hypothesis Testing by Simon Thomas in Stats.

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

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Simon Thomas 5 years, 9 months ago

Error in variable testing condition

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Generated value: `number`

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Simon'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

Simon Thomas 5 years, 9 months ago

Error in variable testing condition

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Warning

Generated value: number

Parts

Gap-fill

Generated value: `number`