One sample t-test -SES

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Lauren Frances Desoysa

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Chris Graham

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Has some problems

6 years, 10 months ago

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Chris Graham commented 6 years, 10 months ago

Hi Lauren, can you move this into the sports science project please.

You've left it a bit in the air whether you are testing the student on which type of test to use. A t-test is implied in part (d), so I would either remove that to just say "test statistic" and start the question with a multiple choice asking which type of test is appropriate, or perhaps just state explicitly that the method will be to use a t-test in the statement.

I would split (d) into two parts, one to identify the significance level (also multiple choice) and the second to draw a conclusion from it.

You should split the advice by parts to help the student to easily digest the information.

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Chris Graham 6 years, 10 months ago

Gave some feedback: Has some problems

○

Lauren Frances Desoysa 6 years, 10 months ago

Created this as a copy of Small sample t-test on sample mean.

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

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Question statement

The following is a set of BMI's (Body Mass Index) for 15 overweight children aged 5.

The data is thought to follow a normal distribution.

{r1[0]}

{r1[1]}

{r1[2]}

{r1[3]}

{r1[4]}

{r1[5]}

{r1[6]}

{r1[7]}

{r1[8]}

{r1[9]}

{r1[10]}

{r1[11]}

{r1[12]}

{r1[13]}

We want to test the hypothesis that the population mean equals $\var{mu1}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

sample_size	integer	15
r1		Expression can't be evaluated -- missing an operator.
sample_mean_2		Error computing referenced variable `r1`
sample_stdev_2		Error computing referenced variable `r1`
mu1	number	17.18
sigm1	number	0.95
test_statistic		Error evaluating variable test_statistic: Variable `sample_mean_2` is not defined.
t95	number	2.145
scenario		Error evaluating variable scenario: Variable `test_statistic` is not defined.
decision_matrix		Error evaluating variable decision_matrix: Variable `scenario` is not defined.
t99	number	2.977
t90	number	1.761
t999	number	4.14
abs		Definition of variable `abs` is empty.

Automatically regenerate variables?

Name

Data type

Value

(a number)

Description

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

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Generated value: `integer`

→ Used by:

test_statistic

This variable doesn't seem to be used anywhere.

Advice

The hypotheses that we are testing are:

$ H_0: \mu=\var{mu1} $ , $ H_1: \mu \neq \var{mu1} $

The test statistic for a one-sample t-test is given by:

$ |t| = \frac{\bar{x}-\mu_0}{s/\sqrt{n}} $

where $\bar{x}$ is the sample mean, given by:

$\bar{x}= \sum_{i=1}^{i=15} \frac{x_i}{15} = \var{sample_mean_2}$ $(2dp)$

and $s$ is the sample standard deviation, given by:

$ s = \sqrt{\frac{\left (\sum (x-\bar{x})^2\right)}{n-1}} = \var{sample_stdev_2}$ $(2dp)$

Therefore, the test statistic is:

$ |{t}| = \frac{\var{sample_mean_2}-\var{mu1}}{\var{sample_stdev_2}/\sqrt{15}}$

$ = \var{abs({test_statistic})} $ $(2dp)$

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

\[\begin{array}{r|rrrr}&0.10&0.05&0.01\\\hline13&\pm\var{t90}&\pm\var{t95}&\pm\var{t99}\end{array}\]

If $ |t| < t_{14}(0.1) $, then we accept $ H_0$ at the 10% level.

If $ |t| > t_{14}(0.1)$, then we reject $H_0$ at the 10% level.

If $ |t| > t_{14}(0.05) $, we reject $H_0$ at the $5%$ level.

If $ |t| > t_{14}(0.01)$, then we reject $H_0$ at the 1% level.

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Chris Graham commented 6 years, 10 months ago

Chris Graham 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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One sample t-test -SES

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Chris Graham commented 6 years, 10 months ago

Chris Graham 6 years, 10 months ago

Lauren Frances Desoysa 6 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`