A-LevelMathematicsProbability and statistics9709/63 · May/June 2020 · Q79 Marks
A market researcher is investigating the length of time that customers spend at an information desk. He plans to choose a sample of 50 customers on a particular day.
- (a)He considers choosing the first 50 customers who visit the information desk. Explain why this method is unsuitable.[1]
- (b)State the probability of making a Type I error and explain what is meant by a Type I error in this context.[2]
- (c)Given that the mean time spent at the information desk by the 50 customers is 6.8 minutes, carry out the test.[5]
- (d)Give a reason why it was necessary to use the Central Limit theorem in your answer to part (c).[1]
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] (a) Later customers might spend times different from first ones
- [B1] (b) 0.02
- [B1] (b) Concluding that µ ≠ 6.0, when actually µ = 6.0
- [B1] (c) H₀: µ = 6.0 H₁: µ ≠ 6.0
- [M1] (c) (6.8 – 6.0) / √ (4.8/50)
- [A1] (c) 2.582
- [M1] (c) comp 2.326
- [A1] (c) Evidence that µ ≠ 6.0
- [B1] (d) Population distribution unknown
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