CAIE A-Level Mathematics 6.5.3 Hypothesis Tests for a Population Mean

CAIE A-Level Mathematics 6.5.3 Hypothesis Tests for a Population Mean
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise testing a population mean from a normal population with known variance or a large sample by forming hypotheses, standardising the sample mean and interpreting…

How this is tested

  • state H₀: μ = μ₀ and choose the one- or two-tailed alternative from the claim
  • standardise x̄ with (x̄ − μ₀)/(σ/√n), estimating σ only when the large-sample rule permits
  • compare the z-value or tail probability with the critical level and conclude in context

Question 2

[Maximum number: 8]

The mean mass of packets of Trueleaf tea is supposed to be 500 grams. An inspector wishes to test whether this value is correct. He weighs 60 randomly chosen packets and notes the mass, x grams, of each packet. The results are summarised as follows.

n=60∑x=29970∑x2=14970300n=60 \quad \sum x=29970 \quad \sum x^{2}=14970300

Test, at the 5% significance level, whether the population mean mass is 500 grams.