May/June 2026 Paper 63

2026 · 6 questions · 14 parts · 50 marks

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Q1
1
–/3 mks
Q2
2(a)2(b)
–/6 mks
Q3
3
–/6 mks
Q4
4(a)4(b)4(c)4(d)
–/11 mks
Q5
5(a)5(b)5(c)5(d)
–/14 mks
Q6
6(a)6(b)
–/10 mks
Context for question 5
The lengths, , of Wamba snakes have mean . Research has shown that, for the whole population of Wamba snakes, . A researcher claims that, for the Wamba snakes in a particular region, the mean length is less than 41.5. She measures the lengths of a random sample of 150 Wamba snakes in this region. The results are summarised below.
5(a)Point Estimation Unbiased EstimatorsMedium3 marks
Find unbiased estimates of the population mean and variance of for Wamba snakes in this region, showing that the unbiased estimate of variance is 64.483 correct to 3 decimal places.
Unbiased estimate of the population mean
Show your method for the variance
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5(b)Hypothesis TestingHard5 marks
Assuming that for the whole population of Wamba snakes, test the researcher’s claim at the 2% significance level.
State your hypotheses
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Show your method
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Test statistic
State your conclusion
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5(c)Hypothesis TestingEasy1 mark
Use your answer to 5(b) to explain whether it is possible for the researcher to make a Type I error.

Answer

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5(d)Hypothesis TestingHard5 marks
Later the researcher carries out a similar test at the 2% significance level, using the same hypotheses and another random sample of 150 Wamba snakes from this region. Given that the population mean length of Wamba snakes for this region is 38.7 cm, find the probability of a Type II error.
Show your method for the critical value
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Critical value of
Show your method
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