Confidence Interval

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Christian Lawson-Perfect

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9 years, 5 months ago

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Christian Lawson-Perfect 9 years, 5 months ago

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Christian Lawson-Perfect 9 years, 5 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 9 years, 5 months ago

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Wrote some advice, changed the notation for confidence intervals.

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Christian Lawson-Perfect 9 years, 5 months ago

Saved a checkpoint:

Rewrote the variables, trying to restore sanity.
The confidence interval for Friday was just made up, so it disagreed with the given data.
Now we pick population means and ranges for Monday and Friday, then generate data from those, and finally calculate the sample statistics. Fortunately, around 50% of the time the confidence intervals overlap.
Still need to write advice, and proofread the question text.

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Hayley Moore 9 years, 8 months ago

Created this.

Name	Status	Author	Last Modified
Confidence Interval	Ready to use	Hayley Moore	01/06/2016 09:47
Confidence Interval Doctor's Surgery	draft	Catherine Palmer	11/11/2018 22:36
Confidence Interval Doctor's Surgery	draft	Catherine Palmer	20/02/2023 11:21
Assessment version Confidence Interval Doctor's Surgery	draft	Catherine Palmer	11/11/2018 22:35
Harry's copy of Confidence Interval Doctor's Surgery	draft	Harry Flynn	15/11/2018 09:55
Sample mean, standard deviation and standard error	draft	Catherine Palmer	20/02/2023 11:19

There are 7 other versions that do you not have access to.

Question statement

The ages of patients coming into a small rural doctor's surgery during the school holidays are noted down on each Monday and Friday thoughout August.

{table([['Monday']+mon,['Friday']+fri],[])}

Give any introductory information the student needs.

			Name	Type	Generated Value

num_monday	integer	12
monday_pop_mean	integer	50
monday_pop_range	integer	20
mon	list	List of 12 items
num_friday	integer	13
friday_pop_mean	integer	61
friday_pop_range	integer	20
fri	list	List of 12 items
monday_mean	number	49.5
monday_sd	number	13.1180537174
monday_se	number	3.7868559225
monday_t	number	2.2009851427
monday_low	number	41.1651863772
monday_high	number	57.8348136228
t	number	2.2009851427
friday_mean	number	65.75
friday_se	number	2.743582255
friday_t	number	2.1788128006
friday_low	number	59.7722478633
friday_high	number	71.7277521367
no_overlap	boolean	true

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
12

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

fri
mon
monday_se
monday_t

This variable doesn't seem to be used anywhere.

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
Part c) Choose one from a list

Gap-fill

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

Calculate the mean and standard deviation of the sample of patients visiting on Mondays.

Enter your answers to 2 decimal places.

Mean: Gap 0.

Standard Deviation: Gap 1.

Advice

a)

The mean of the sample of patients visiting on Mondays is

$\bar{x} = \frac{1}{n}(\sum x_i) = \var{precround(monday_mean,2)} \text{ (to 2 d.p.)}$

The standard deviation is

$s = \sqrt{\frac{1}{n}\sum \left(x_i-\bar{x}\right)^2} = \var{precround(monday_sd,2)} \text{ (to 2 d.p.)}$

b)

The sample mean $\mu_m$ follows a $t$ -distribution with $n-1 = \var{num_monday-1}$ degrees of freedom centred on the population mean, with a standard error of $\frac{s}{\sqrt{n}} = \simplify{{precround(monday_sd,2)}/sqrt({num_monday})} = \var{precround(monday_se,2)}$ .

That means that the 95% confidence interval for the population mean is as follows:

$\begin{array}{lrcl} &\left[ \bar{x} - s \times t_{\var{num_monday-1},0.975} \right. \kern{-0.5em}&,&\kern{-0.5em} \left. \bar{x} + s \times t_{\var{num_monday-1},0.975} \right] \\ = & \left[ \simplify[]{{precround(monday_mean,2)} - {precround(monday_se,2)}*{precround(monday_t,2)}} \right. \kern{-0.5em}&,&\kern{-0.5em} \left. \simplify[]{{precround(monday_mean,2)} + {precround(monday_se,2)}*{precround(monday_t,2)}} \right] \\ = & \left[ \var{precround(monday_low,2)} \right. \kern{-0.5em}&,&\kern{-0.5em} \left. \var{precround(monday_high,2)} \right] \end{array}$

c)

The 95% confidence intervals for the two population means do not overlap, so they must be significantly different.The 95% confidence intervals for the two populations overlap, so we do not have enough evidence to say whether they are significantly different.

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
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Gap-fill
Gap-fill		Hasn't run yet
Number entry
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Number entry
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Choose one from a list
Choose one from a list		Hasn't run yet

This question is used in the following exams:

Confidence Intervals by Hayley Moore in Hayley's workspace.
Hypothesis testing by Catherine Palmer in STAT7008.
Confidence Intervals by Kevin Bohan in Kevin's workspace.
Izabela's copy of Confidence Intervals by Izabela Walczak in Statistics 2020.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Hayley Moore 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

c)

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Confidence Interval

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Christian Lawson-Perfect 9 years, 5 months ago

Hayley Moore 9 years, 8 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

c)

Generated value: `integer`