2012 2013 CBA4_3

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Bill Foster

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Newcastle University Mathematics and Statistics 9 years, 3 months ago

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Name	Status	Author	Last Modified
2012 2013 CBA4_3	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:51
Two sided single sample hypothesis test	draft	Catherine Palmer	25/11/2018 21:32
Hypothesis test of t-distribution	draft	Xiaodan Leng	10/07/2019 22:58

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Question statement

$X_1,\;X_2,\;\dots, X_n$ is a random sample from $\operatorname{N}(\mu,\sigma^2)$.

The sample size is $n=\var{n}$, with sample mean $\bar{x}=\var{r11}$ and $s=\var{sd}$, the sample standard deviation.

Suppose we wish to test at the $\var{le}$% level the null hypothesis $H_0: \mu=\var{tr}$ versus a two sided alternative hypothesis.

Give any introductory information the student needs.

			Name	Type	Generated Value

le	integer	5
that	string	not significant and cannot re
mm	list	[ 0, 1 ]
r11	number	74.4
tr	integer	72
n	integer	20
mu	integer	74
isthis	string	is less than
tol	number	0.001
pert	integer	2
test	number	1.073
st	number	2.093
sd	number	10

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(10,5,1,0.1)

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:

st
that

Statement
Advice

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Choose one from a list
  Add

Gap-fill

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

Calculate the t-statistic you will need to test the null hypothesis:

Test statistic $t=\;$?Unnamed gap (to 3 decimal places).

Advice

The test statistic is given by:

\[t = \frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\]

and in this case we have:

\[t = \frac{\var{r11}-\var{tr}}{\frac{\var{sd}}{\sqrt{\var{n}}}}=\var{test}\] to 3 decimal places.

Now look up in the tables the critical value at $\var{le}$% for $\var{n}-1=\var{n-1}$ degrees of freedom and a two-sided test.

Note that as we are using one-sided tables we have to look at the $1-\var{le}/200=\var{1-le/200}$ critical value and find the corresponding value.

In this case it is $\var{st}$ to 3 decimal places.

Since $\var{abs(test)}$ {isthis} $\var{st}$ we see that the result is {that}.

Give a worked solution to the whole question.

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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
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

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Taxonomy: mathcentre

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Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

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2012 2013 CBA4_3

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`