Perform t-test for hypothesis given sample mean and standard deviation

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Simon Thomas 6 years, 2 months ago

Created this.

Name	Status	Author	Last Modified
Perform t-test for hypothesis given sample mean and standard deviation	draft	Simon Thomas	07/02/2019 10:22
Simon's copy of Perform t-test for hypothesis given sample mean and standard deviation	draft	Simon Thomas	05/06/2019 14:31

Question statement

{this}

{claim}

{test}

A sample of {n} {things}

{resultis} £{m} with a standard deviation of £{stand}.

Perform an appropriate hypothesis test to see if the claim made by the online flight company is substantiated (use a two-tailed test).

Give any introductory information the student needs.

			Name	Type	Generated Value

claim	string	The average cost of a flight w
pval	integer	1
evi1	list	List of 4 items
crit	list	[ 1.833, 2.262, 3.250 ]
tval1	number	2.012358511
things	string	customers is taken.
stand	integer	22
tol	number	0.001
test	string	A rival flight company decides
pm	list	List of 4 items
correctc	string	There is insufficient evidence
resultis	string	The mean cost of a flight to A
here	string	Athens
fac	string	There is sufficient evidence a
confl	integer	95
evi	list	List of 4 items
this	string	An online flight company makes
dothis	string	retain
m	integer	90
dmm	list	[ 1, 0 ]
n	integer	10
mm	list	[ 0, 1, 0, 0 ]
thisamount	integer	76
tval	number	2.012

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
"The average cost of a flight with us to "+ here + " is just £" + {thisamount} + " (including all taxes and charges!)"

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 average cost of a flight with us to Athens is just £76 (including all taxes and charges!)

← Depends on:

here
thisamount

→ 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

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

Advice

Step 1: Null Hypothesis

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

Step 2: Alternative Hypothesis

$\operatorname{H}_1\;: \; \mu \neq\;\var{thisamount}$

We should use the t statistic as the population variance is unknown.

The test statistic:

\[t =\frac{ |\var{m} -\var{thisamount}|} {\sqrt{\frac{\var{stand} ^ 2 }{\var{n}}}} = \var{tval}\]

to 3 decimal places.

As $n=\var{n}$ we use the $t_{\var{n-1}}$ tables. We have the following data from the tables:

{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 t-test for hypothesis given sample mean and standard deviation

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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 t-test for hypothesis given sample mean and standard deviation

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`