Calculate confidence interval for the proportion

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Catherine Palmer 6 years, 5 months ago

Created this as a copy of Calculate confidence interval for the mean, sample variance n>30.

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Question statement

{scenario1[Index]} {n1[Index]} {scenario2[Index]} {prop1[Index]} {scenario3[Index]} {percentage}% {scenario4[Index]}.

Give any introductory information the student needs.

			Name	Type	Generated Value

scenario1	list	List of 2 items
scenario2	list	List of 2 items
prop1	list	[ 75, 42 ]
scenario3	list	List of 2 items
p_hat	rational	3/4
n1	list	[ 100, 190 ]
scenario4	list	List of 2 items
alpha2	rational	1/20

			Name	Type	Generated Value

upper	decimal	dec("0.834870489570875")
Index	integer	0
percentage	integer	95
Z	number	1.96
alpha	rational	1/40
lower	decimal	dec("0.665129510429125")
se	decimal	dec("0.0433")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["A survey of","A manufacturer would like to estimate the proportion of X-ray machines that malfunction and produce excess radiation. A random sample of"]
​
​

JME function reference

Description

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

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Generated value: `list`

[ "A survey of", "A manufacturer would like to estimate the proportion of X-ray machines that malfunction and produce excess radiation. A random sample of" ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Gap 0. Number entry
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2. Gap Gap 1. Number entry
  Add

Gap-fill

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Lower limit = Gap 0.

Upper limit = Gap 1.

Advice

The estimate for the population proportion is $\hat{p} =\frac{{\var{prop1[Index]}}}{\var{n1[Index]}}=\var{precround(p_hat,3)}$

The estimate for the standard error associated with $\hat{p}$ is $=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}=\sqrt{\frac{\var{precround(p_hat,3)}\times (1-\var{precround(p_hat,3)})}{\var{n1[Index]}}}=\var{se}$

To construct a $\var{percentage}$ % confidence interval, $Z_\frac{\alpha}{2}=Z_\frac{\var{alpha2}}{2} = \var{Z}$

Putting this information together, the lower bound of the $\var{percentage}$ % confidence interval is:

$\hat{p} -Z_\frac{\alpha}{2}\times\sqrt{\frac{\hat{p}(1-\hat{p})}{\var{n1[Index]}}}=\var{precround(p_hat,3)} -\var{Z}\times \var{se}=\var{precround(lower,2)}$

The upper bound of the $\var{percentage}$ % confidence interval is:

$\hat{p} +Z_\frac{\alpha}{2}\times\sqrt{\frac{\hat{p}(1-\hat{p})}{\var{n1[Index]}}}=\var{precround(p_hat,3)} +\var{Z}\times \var{se}=\var{precround(upper,2)}$

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Calculate confidence interval for the proportion

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Taxonomy: mathcentre

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Catherine Palmer 6 years, 5 months ago

Error in variable testing condition

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Generated value: `list`

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Error

Calculate confidence interval for the proportion

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Catherine Palmer 6 years, 5 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`