Perform a one-sample t-test

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From users who are members of Newcastle University Sports Science :

George Stagg	said	Needs to be tested	4 years, 4 months ago
Tom Lowe	said	Doesn't work	4 years, 4 months ago
Lauren Frances Desoysa	said	Needs to be tested	6 years, 10 months ago

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Tom Lowe commented 4 years, 4 months ago

Question now works fine. I've made some corrections to the advice, by ensuring that the modulus signs are in the calculation of the absolute value of T, and changing part e) to say that we reject the null hypothesis if our test is significant at the 5% level, as is consistent with the marking (it previously said to reject if the test was significant at the 10% level).

I think the question would benefit from adaptive marking, but can't see any other issues.

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George Stagg commented 4 years, 4 months ago

The question had broken with Numbas updates. I think I've fixed the scenario variable, but didn't test the question in detail so have marked "needs to be tested" for now.

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George Stagg 4 years, 4 months ago

Gave some feedback: Needs to be tested

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Tom Lowe commented 4 years, 4 months ago

When trying to test run the question I get an error, and in the variables section the variable "scenario" is not defined, with the following error message:

Error evaluating variable scenario: No definition of 'sum' of correct type found.

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Tom Lowe 4 years, 4 months ago

Gave some feedback: Doesn't work

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Chris Graham commented 6 years, 9 months ago

Thanks Lauren, can you check with Phil regarding the wording of the last part. I think (I'm no statistician) that you are not supposed to "accept" a null hypothesis, rather you "do not reject" it.

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Christian Lawson-Perfect was given access to the Perform a one-sample t-test 6 years, 10 months ago

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Lauren Frances Desoysa commented 6 years, 10 months ago

Hi chris, there's a couple of things that probably need changing, such as alligning the equals signs in the advise solution, but other than that i think i've made all the changes you wanted.

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Lauren Frances Desoysa 6 years, 10 months ago

Gave some feedback: Needs to be tested

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Lauren Frances Desoysa 6 years, 10 months ago

Created this as a copy of One sample t-test -SES.

Name	Status	Author	Last Modified
Small sample t-test on sample mean	Ready to use	Frank Doheny	21/02/2023 07:50
Two sample t-test: comparison of means	Ready to use	Frank Doheny	07/10/2021 10:29
Two sample t-test: paired data	Ready to use	Frank Doheny	07/10/2021 10:24
Z-test on sample mean	Ready to use	Frank Doheny	04/10/2021 21:48
Z-test on sample proportion	Ready to use	Frank Doheny	04/10/2021 22:24
Two sample Z-test on proportions	Ready to use	Frank Doheny	07/10/2021 10:40
Chi-square goodness of fit test	Ready to use	Frank Doheny	21/02/2023 07:39
Chi-square test: contingency tables	Ready to use	Frank Doheny	08/10/2021 14:55
ANOVA	Ready to use	Frank Doheny	21/02/2023 07:50
One sample t-test -SES	Has some problems	Lauren Frances Desoysa	25/06/2018 09:49
Perform a one-sample t-test	Needs to be tested	Lauren Frances Desoysa	11/11/2024 14:22
Colin's copy of Two sample t-test: paired data	draft	Colin Whitehead	25/06/2018 15:31
David's copy of Z-test on sample mean	draft	David Goulding	18/09/2018 16:33
Resting heart rate statistics	draft	David Goulding	18/09/2018 16:54
Catherine's copy of Z-test on sample proportion	draft	Catherine Palmer	13/03/2022 22:33
STAT7008 Hypothesis test, single sample, two sided t-test on sample mean	draft	Catherine Palmer	25/11/2020 19:04
Charlie's copy of STAT7008 Hypothesis test, single sample, two sided t-test on sample mean	draft	Charlie Earle	09/12/2018 12:34
Two sample t-test: Paired data	Should not be used	Brad Allison	11/06/2020 14:14
Brad's copy of Two sample t-test: comparison of means	draft	Brad Allison	12/06/2019 12:40
Brad's copy of Two sample t-test: paired data	draft	Brad Allison	13/06/2019 14:01
ANOVA	draft	Xiaodan Leng	11/07/2019 00:17
Chi-square test: contingency tables	draft	Xiaodan Leng	11/07/2019 00:17
Chi-square goodness of fit test	draft	Xiaodan Leng	11/07/2019 00:17
Z-test on sample proportion	draft	Xiaodan Leng	11/07/2019 00:18
Z-test on sample mean	draft	Xiaodan Leng	11/07/2019 00:18
Two sample Z-test on proportions	draft	Xiaodan Leng	11/07/2019 00:19
Two sample t-test: paired data	draft	Xiaodan Leng	11/07/2019 00:19
Two sample t-test: comparison of means	draft	Xiaodan Leng	11/07/2019 00:20
Small sample t-test on sample mean	draft	Xiaodan Leng	11/07/2019 00:20
Chi-square goodness of fit test	Ready to use	Ben Parker	24/02/2023 11:16

There are 50 other versions that do you not have access to.

Question statement

The following is a set of BMIs (Body Mass Index) for $\var{sample_size}$ overweight children aged $5$ .

The data is thought to follow a normal distribution.

$\var{r1[0]}$

$\var{r1[1]}$

$\var{r1[2]}$

$\var{r1[3]}$

$\var{r1[4]}$

$\var{r1[5]}$

$\var{r1[6]}$

$\var{r1[7]}$

$\var{r1[8]}$

$\var{r1[9]}$

$\var{r1[10]}$

$\var{r1[11]}$

$\var{r1[12]}$

$\var{r1[13]}$

$\var{r1[14]}$

Using a one sample $t$ -test, test the hypothesis that the population mean equals $\var{mu_hyp}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

t95	number	2.145
t99	number	2.977
t999	number	4.14
t90	number	1.761

			Name	Type	Generated Value

sample_size	integer	15
r1	list	List of 15 items
test	list	List of 15 items

			Name	Type	Generated Value

			sample_stdev	number	0.72874125
			sample_mean	number	17.3573333333

			Name	Type	Generated Value

mu1	number	17.35
sigm1	number	0.65
mu_hyp	integer	17
test_statistic	number	1.9099643899
scenario	number	1
decision_matrix	list	[ 0, 1, 0, 0 ]
reject_matrix	list	[ 1, 0 ]
abs	number	1.9099643899

Automatically regenerate variables?

Name

Data type

Value

(a number)

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: `number`

2.145

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
  Add
Part d) Choose one from a list
Part e) Choose one from a list

Gap-fill

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

Calculate the sample mean, $\bar{x}$.

$\bar{x} = $ Unnamed gap

Advice

(a)

The sample mean, $\bar{x}$, is given by

\[ \bar{x}= \sum_{i=1}^{15} \frac{x_i}{15} = \var{dpformat(sample_mean,2)}\text{,} \]

to 2 decimal places.

(b)

The sample standard deviation, $s$, is given by

\[ s = \sqrt{\frac{\left (\sum (x-\bar{x})^2\right)}{n-1}} = \var{dpformat(sample_stdev,2)}\text{,} \]

to 2 decimal places.

(c)

The t-test statistic is

\[|{T}| = \frac{| \var{dpformat(sample_mean,2)}-\var{mu_hyp}|}{\var{dpformat(sample_stdev,2)}/\sqrt{\var{sample_size}}}
= \var{dpformat(abs({test_statistic}),2)}\text{,} \]

to 2 decimal places.

(d)

The hypotheses that we are testing are:

\begin{align}
H_0: \mu &=\var{mu_hyp}\text{,} \\
H_1: \mu &\neq \var{mu_hyp}\text{.}
\end{align}

The t-table values will be for a two-tailed test and will have $ n-1 = 14$ degrees of freedom:

\[\begin{array}{r|rrrr}&0.10&0.05&0.01\\\hline14&\var{t90}&\var{t95}&\var{t99}\end{array}\]

If $ |T| < t_{\simplify{{sample_size}-1}}(0.1) $, then the test is not significant at the 10% level.

If $ t_{\simplify{{sample_size}-1}}(0.1) < |T| < t_{\simplify{{sample_size}-1}}(0.05) $, then the test is significant at the 10% level but not the 5% level.

If $ t_{\simplify{{sample_size}-1}}(0.05) < |T| < t_{\simplify{{sample_size}-1}}(0.01) $, then the test is significant at the 5% level but not the 1% level.

If $ |T| > t_{\simplify{{sample_size}-1}}(0.01) $, then the test is significant at the 1% level.

(e)

If the test is not significant at the 5% level, then we do not reject $ H_0$, otherwise we reject $H_0$.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

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Tom Lowe commented 4 years, 4 months ago

George Stagg commented 4 years, 4 months ago

George Stagg 4 years, 4 months ago

Tom Lowe commented 4 years, 4 months ago

Tom Lowe 4 years, 4 months ago

Chris Graham commented 6 years, 9 months ago

Christian Lawson-Perfect was given access to the Perform a one-sample t-test 6 years, 10 months ago

Lauren Frances Desoysa commented 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `number`

Parts

Gap-fill

(a)

(b)

(c)

(d)

(e)

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Perform a one-sample t-test

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Tom Lowe commented 4 years, 4 months ago

George Stagg commented 4 years, 4 months ago

George Stagg 4 years, 4 months ago

Tom Lowe commented 4 years, 4 months ago

Tom Lowe 4 years, 4 months ago

Chris Graham commented 6 years, 9 months ago

Christian Lawson-Perfect was given access to the Perform a one-sample t-test 6 years, 10 months ago

Lauren Frances Desoysa commented 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: number

Parts

Gap-fill

(a)

(b)

(c)

(d)

(e)

Generated value: `number`