CAIE A-Level Mathematics A2 6.5.5 Normal Distribution Questions
Practise calculating Type II error probabilities under specified alternative parameter values.
- Syllabus
- 2028–2030
- Course
- Mathematics 9709
- Level
- A2
Exam points
- identify the acceptance region for a hypothesis test
- calculate Type II error probabilities under an alternative hypothesis
- interpret the power and error probabilities of a test
CAIE A-Level Mathematics A2 6.5.5 Normal Distribution Questions question 1
[Maximum number: 5]
The heights, in centimetres, of adult females in Litania have mean μ and standard deviation σ. It is known that in 2004 the values of μ and σ were 163.21 and 6.95 respectively. The government claims that the value of μ this year is greater than it was in 2004. In order to test this claim a researcher plans to carry out a hypothesis test at the 1% significance level. He records the heights of a random sample of 300 adult females in Litania this year and finds the value of the sample mean.
Given that the value of μ this year is actually 164.91, find the probability of a Type II error.
2.326=h-163.216.95 / 300
Marking guidance:
Accept any z( +/-).
h=164.14
[Rejection region is h>164.14][P ( Type II )=P(h<164.14 µ=164.91) ]
Accept 3 sf accuracy here.
their ^ 164.14 ^-164.916.95 / 300 [=-1.919]
For standardising 164.91 with their 164.14 (could be 163.21).
(. their .^6-1.919^)=1-(. their .^6 1.919^)
For area attempt consistent with their values.
=0.0275 or 0.0276 or 0.028 [0] (3.s.f)
Accept anything in range 0.0275 to 0.028[0].
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