One-sample test: lead concentration

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Andrea Wilmshurst

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2 weeks, 5 days ago

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Andrea Wilmshurst 2 weeks, 5 days ago

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Mario Orsi 4 years, 3 months ago

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Mario Orsi 5 years, 3 months ago

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Name	Status	Author	Last Modified
One-sample test: lead concentration	Ready to use	Mario Orsi	07/04/2025 16:24
CI for a difference of means: embryonic stem cells	Ready to use	Mario Orsi	29/01/2025 10:08
Mitchum's copy of CI for a difference of means: embryonic stem cells	Ready to use	Mitchum Bock	23/06/2020 17:27
Test istotności dla dwóch średnich	Ready to use	Aleksandra Romanowska	16/06/2021 21:28

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Question statement

Consider a random sample of $\var{n}$ traffic officers, who regularly inhale high levels of car exhaust fumes as part of their job. Blood samples from these officers show an average lead concentration of $\var{mean}$ $\mu$ g/l and a standard deviation of $\var{sd}$ $\mu$ g/l. A previous study of individuals with no history of high exposure to car fumes found an average blood level concentration of $\var{mu0}$ $\mu$ g/l. Consider a proposed hypothesis that traffic officers are exposed to significantly different concentrations of lead than normal.

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	22
mu0	integer	30
mean	integer	49
sd	integer	44
CL	integer	90
ciLower	number	65.1
ciUpper	number	32.9
se	number	9.38
tol	number	0.05
T	number	2.03
p	number	0.0552
tStar	number	-1.72

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random(10..50)

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Description

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

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Generated value: `integer`

This variable doesn't seem to be used anywhere.

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

Calculate the standard error:

Unnamed gap$\mu$g/l

Advice

Revise the one-sample t-test, e.g., Section 7.1 of OpenIntro Statistics (4th edition).

a) The standard error (SE) is:

$SE=\frac{SD}{\sqrt{n}}$

with $SD$ the standard deviation and $n$ the sample size.

b) The appropriate $t^*$ can be obtained using the Excel function T.INV.2T, with $df=n-1$.

c) The $T$ statistic is:

$T=\frac{\bar{x}-\mu_0}{SE}$

with $\bar{x}$ the sample mean and $\mu_0$ the hypothesized mean.

d) The $p$-value can be calculated with the Excel function T.DIST.2T, with the $T$ statistic and the number of degrees of freedom as arguments.

Give a worked solution to the whole question.

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This question is used in the following exams:

Exam4SAT by Mario Orsi in Trash-backup.
Exam May 2021 by Mario Orsi in Stats.
Sarah's copy of Exam May 2021 by Sarah Dean in Applied Scientific Practice.

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Taxonomy: mathcentre

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Checkpoint description

Andrea Wilmshurst 2 weeks, 5 days ago

Mario Orsi 4 years, 3 months ago

Mario Orsi 5 years, 3 months ago

Error in variable testing condition

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Generated value: `integer`

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Gap-fill

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One-sample test: lead concentration

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Andrea Wilmshurst 2 weeks, 5 days ago

Mario Orsi 4 years, 3 months ago

Mario Orsi 5 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`