The t-distribution: application

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Question statement

An independent random sample of size $n=\var{n}$ is selected from an approximately normal population with unknown standard deviation.

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	28
CL	integer	90
t	number	1.70
tol	number	0.05
tStat	number	2.83
p	number	0.00868

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(10..30)

JME function reference

Description

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

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Generated value: `integer`

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Statement

Advice

a) The number of degrees of freedom is $n-1$.

An $x\%$ confidence level corresponds to a two tails probability of $(100-x)\%=(100-x)/100$.

The critical value $t^\star$ can now be obtained using statistical tables or software, e.g., the T.INV.2T Excel function.

b) For a two-tailed test (which is the most common case), the $p$-value represents the probability in the tails of the $t$-distribution for a given test statistic, i.e., the proportion of the distribution falling more than $T$ units away from the mean.

This can be obtained with software tools such as the T.DIST.2T Excel function.

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This question is used in the following exams:

Exam May 2021 by Mario Orsi in Stats.
Sarah's copy of Exam May 2021 by Sarah Dean in Applied Scientific Practice.
ResitExam20Qs by Mario Orsi in Stats.
SP test 2 by Mario Orsi in Stats.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Mario Orsi 5 years, 3 months ago

Mario Orsi 5 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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Number entry

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The t-distribution: application

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mario Orsi 5 years, 3 months ago

Mario Orsi 5 years, 3 months ago

Mario Orsi 5 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Number entry

Advanced settings

Generated value: `integer`