Confidence Interval

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Ruth Hand

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2 years, 8 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

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Ruth Hand 2 years, 8 months ago

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Ruth Hand 4 years, 1 month ago

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Question statement

A sample of size $n = \var{n}$ produced a sample mean of $\bar{x} = \var{xbar}$ .

Assuming the population standard deviation $\sigma = \var{sigma}$ , compute a 95% confidence interval for the population mean, $\mu$ .

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			Name	Type	Generated Value

n	integer	134
xbar	number	69.904
sigma	number	9.1
ci_percent	integer	95
alp	rational	1/40
mu	number	69.6
ci_lower	number	68.36
ci_upper	number	71.44

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Generated value: `integer`

134

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ci_lower
ci_upper

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A 95% confidence interval for $\mu$ is

\[ \big[ \bar{x} - z_{\alpha/2} \frac{\sigma}{\sqrt{n}} , \bar{x} + z_{\alpha/2} \frac{\sigma}{\sqrt{n}} \big] \]

Where $\alpha = 0.05$, (because $95\% = 0.95$ and $1-0.95 = 0.05)$, is the probability of a value lying outside the confidence interval and $z_{\alpha/2}$ is the lower bound z-value for the confidence interval, i.e. $P(Z < z_{\alpha/2}) = 0.975$.

We know that:

$z_{{\alpha}/2} = z_{0.025} = 1.96$ (from the table of Normal distribution),

Therefore, the 95% confidence interval for µ will be:

\[ \big[ \var{xbar} - 1.96 \times \frac{\var{sigma}}{\sqrt{\var{n}}} ,\var{xbar} + 1.96 \times \frac{\var{sigma}}{\sqrt{\var{n}}} \big] \]

\[ [ \var{ci_lower} , \var{ci_upper} ] \]

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This question is used in the following exams:

CI exam by Ruth Hand in MASH Bath: Moodle quizzes and TS.
MA5636 Week3 by Ben Parker in Ben's workspace.
Basic statistics by Jinhua Mathias in Statistics 2020.
Mathematics for Data Science Class Test 1 by Rabail Tahir in Rabail's workspace.
Mathematics in Data Science Class test 1 by Rabail Tahir in Rabail's workspace.

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Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 8 months ago

Ruth Hand 4 years, 1 month ago

Error in variable testing condition

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Generated value: `integer`

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Confidence Interval

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 8 months ago

Ruth Hand 4 years, 1 month ago

Error in variable testing condition

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Generated value: integer

Parts

Gap-fill

Generated value: `integer`