Confidence Interval Doctor's Surgery

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Catherine Palmer 6 years, 4 months ago

Created this as a copy of Confidence Interval Doctor's Surgery.

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 a random sample of patients coming into a 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	33
monday_pop_range	integer	20
mon	list	List of 12 items
num_friday	integer	14
friday_pop_mean	integer	52
friday_pop_range	integer	20
fri	list	List of 12 items
monday_mean	number	30.1666666667
monday_sd	number	12.0365604671
monday_se	number	3.4746557129
monday_t	number	2.2009851427
monday_low	number	22.5190010667
monday_high	number	37.8143322666
t	number	2.2009851427
friday_mean	number	54
friday_se	number	2.5609454423
friday_t	number	2.1603686523
friday_low	number	48.4674137462
friday_high	number	59.5325862538
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`

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

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

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

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:

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

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This question is used in the following exams:

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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History

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Checkpoint description

Catherine Palmer 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

a)

b)

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Confidence Interval Doctor's Surgery

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Catherine Palmer 6 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

a)

b)

Generated value: `integer`