Z-test on sample mean

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Xiaodan Leng 5 years, 10 months ago

Created this as a copy of Z-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

A sample of 30 deaths of men in Ireland during the past year was selected at random and the ages of each man at the time of death recorded. The data collected is presented below.

{r1[0]}

{r1[1]}

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{r1[22]}

{r1[29]}

{r1[23]}

{r1[24]}

{r1[25]}

{r1[26]}

{r1[27]}

{r1[28]}

It is believed that the mean lifespan for Irish men is $\simplify{{mu1}-{k}}$ years.

Does the data support this theory?

Give any introductory information the student needs.

			Name	Type	Generated Value

sample_size	integer	30
r1	list	List of 30 items
decision_matrix		Error evaluating variable decision_matrix: Variable `scenario` is not defined.
sample_mean_2	number	73.30
sample_stdev_2	number	6.70
mu1	number	73
scenario		Error evaluating variable scenario: No definition of 'sum' of correct type found.
sigm1	number	5.5
t95	number	1.96
t99	number	2.58
k	number	1
t90	number	1.65
test_statistic	number	1.06

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: `integer`

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) Choose one from a list

Gap-fill

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

Give all your answers correct to two decimal places.

Input the sample mean: $\bar{x}=$ Gap 0.

Input the sample standard deviation: $s=$ Gap 1.

Enter the value for the test statistic: $Z=$ Gap 2.

Advice

In this example we have a single sample of 30 data values. The sample is just large enough to apply a Z-test

$H_0:$ The mean $=\simplify{{mu1}-{k}}$.

$H_1:$ The mean $\ne \simplify{{mu1}-{k}}$.

Given a sample of size $n$ recall:

the formula for the sample mean: $\overline{x}=\frac{\sum {x}}{n}=\var{sample_mean_2}$

the formula for the sample standard deviation: $s=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n-1}}=\var{sample_stdev_2}$

the formula for the Z-statistic: $Z=\frac{\overline{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{\var{sample_mean_2}-\simplify{{mu1}-{k}}}{\frac{\var{sample_stdev_2}}{\sqrt{\var{sample_size}}}}=\var{test_statistic}$

The Z-table values will be for a two-tailed test are given below.

significance 10% 5% 1%

limits $\pm1.65$ $\pm1.96$ $\pm2.58$

Compare the test statistic with the Z-table values and choose your conclusion.

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
Number entry
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Number entry
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Choose one from a list
Choose one from a list		Hasn't run yet

This question is not used in any exams.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Checkpoint description

Xiaodan Leng 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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Error

Z-test on sample mean

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Xiaodan Leng 5 years, 10 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`