Assessment: 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 proportion.

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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	[ 250, 70 ]
scenario3	list	List of 2 items
p_hat	rational	25/52
n1	list	[ 520, 220 ]
scenario4	list	List of 2 items
alpha2	rational	1/100

			Name	Type	Generated Value

upper	decimal	dec("5.372976156338527692307692307692307692308e-1")
Index	integer	0
percentage	integer	99
Z	number	2.58
alpha	rational	1/200
lower	decimal	dec("4.242408459046087692307692307692307692308e-1")
se	decimal	dec("0.0219")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
["A poll to determine which candidate is ahead in a two candidate election surveys","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 poll to determine which candidate is ahead in a two candidate election surveys", "A random sample of" ]

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Statement

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

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

The estimate for the population proportion $\hat{p}=$ Gap 0.

The estimate for the standard error of the sample proportion = 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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Assessment: calculate confidence interval for the proportion

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Catherine Palmer 6 years, 5 months ago

Error in variable testing condition

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Warning

Generated value: `list`

Parts

Gap-fill

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Error

Assessment: 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`