A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2021 · Q34 Marks
An architect wishes to investigate whether the buildings in a certain city are higher, on average, than buildings in other cities. He takes a large random sample of buildings from the city and finds the mean height of the buildings in the sample. He calculates the value of the test statistic, z, and finds that z = 2.41.
- (a)Explain briefly whether he should use a one-tail test or a two-tail test.[1]
- (b)Carry out the test at the 1% significance level.[3]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2021). The mark or mark type is shown in brackets.
- [B1] One-tail because investigating whether "higher"
- [B1] Ho: Population mean (or u) in city same as for others
- [B1] H1: Population mean (or u) in city greater than for others
- [M1] 2.41 > 2.326 or 0.008 < 0.01 or 0.992 > 0.99
- [A1] There is evidence that buildings are higher [on average].
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