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Hypothesis testing
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122 questions at your level
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Level 2
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Setting up a hypothesis test
18 questions
Lesson
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Mark as done
A manufacturer claims that
30
%
30\%
30%
of its chocolates are dark. A sample of
20
20
20
is taken to test whether the proportion of dark chocolates is greater than claimed. Let
X
X
X
be the number of dark chocolates and
p
p
p
the population proportion.
(a)
State the null and alternative hypotheses.
(b)
State the distribution of
X
X
X
under the null hypothesis.
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Level 2
3 marks
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Mark as done
In a binomial hypothesis test, explain what is meant by
(a)
the test statistic, and (b) the significance level.
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Level 2
2 marks
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Critical regions and actual significance level
28 questions
Lesson
Not started
Mark as done
The random variable
Y
Y
Y
has a Poisson distribution with mean
λ
\lambda
λ
. A single observed value of
Y
Y
Y
is to be used to test
H
0
:
λ
=
3.5
H_0: \lambda = 3.5
H
0
:
λ
=
3.5
against
H
1
:
λ
<
3.5
H_1: \lambda < 3.5
H
1
:
λ
<
3.5
, using a
5
%
5\%
5%
level of significance.
(a)
Find the critical region for this test.
(2 marks)
(b)
Write down the actual significance level of this test.
(1 mark)
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Level 2
3 marks
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