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2.5.8 Hypothesis test for a single mean (A-level only)

2.5.8 Hypothesis test for a single mean (A-level only)

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Question 23

A machine fills bottles with water. The amount of water in each bottle, W W\,W ml, is normally distributed with mean 500 ml. Given that 30% of bottles contain more than 504 ml

a.

Find the value of k k\,k such that P(k<W<505)=0.45P(k < W < 505) = 0.45P(k<W<505)=0.45

[5]
b.

The machine is adjusted so that the standard deviation of the amount of water in each bottle is now 6 ml. Following the adjustments the company manager now believes that the mean amount of water in each bottle is less than 500 ml. She takes a random sample of 20 bottles and finds the mean amount of water to be 498.1 ml. Test the company manager's belief at the 5% significance level. You should state your hypotheses clearly.

[5]
Markscheme

2.5.8 Hypothesis test for a single mean (A-level only) Questions

  1. A Level
  2. /Maths
  3. /2.5.8 Hypothesis test for a single mean (A-level only)

132 exam-style questions on OCR (MEI) A Level Maths 2.5.8 Hypothesis test for a single mean (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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