Confidence interval - marijuana survey - Numbas at mathcentre.ac.uk

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Question statement

In a recent survey, $\var{n}$ UK adults were asked: "Do you think the use of marijuana should be legalized?"

$\var{percentage}\%$ of the respondents said it should.

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	513
percentage	integer	65
CI_low	number	60.9
se	decimal	dec("2.105872231582554328789980684673015760714e-2")
p	rational	13/20
CI_high	number	69.1
nMin	decimal	dec("8740")
MoE_limit	number	0.01

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(100..999)

JME function reference

Description

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Generated value: `integer`

513

→ Used by:

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Parts

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

Gap-fill

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Construct a $95\%$ confidence interval for the proportion of UK adults who think marijuana should be legalized (rounding to 1 decimal place):

( Gap 0.% , Gap 1.% )

Advice

For general background, see relevant textbook sections on Confidence Intervals (e.g., Chapter 5 in OpenIntro Statistics).

a) The standard error for a proportion is $SE=\sqrt{\frac{p(1-p)}{n}}$ , with $p$ the proportion (as a number between 0 and 1, not as a percentage), and $n$ the sample size.

The margin of error is $MoE=z^\star\times SE$ , with $z^\star$ the appropriate z-value (e.g., $z^\star = 1.96$ for a $95\%$ confidence level).

The confidence interval is: $(p-MoE, p+MoE)$ .

b) To limit the MoE to $1\%$ , the sample size $n$ must satisfy this equation:

$1.96\times\sqrt{\frac{p(1-p)}{n}}=0.01$

Solving for $n$ gives the required sample size.

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This question is used in the following exams:

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Confidence interval - marijuana survey

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Taxonomy: mathcentre

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Taxonomy: Context

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Mario Orsi 5 years ago

Mario Orsi 5 years, 3 months ago

Mario Orsi 5 years, 6 months ago

Error in variable testing condition

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Generated value: `integer`

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Confidence interval - marijuana survey

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Mario Orsi 5 years ago

Mario Orsi 5 years, 3 months ago

Mario Orsi 5 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`