ConceptConceptDocsDocuments

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

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…

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • 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

6.5.3—Hypothesis tests question 1

[Maximum number: 5]

The score on one spin of a 5 -sided spinner is denoted by the random variable X with probability distribution as shown in the table.

Table for Question 6.5.3—Hypothesis tests question 1 — CAIE A-Level Mathematics A2

Johann has another, similar, spinner. He suspects that it is biased so that the mean score is less than 2 . He spins his spinner 200 times and finds that the mean of the 200 scores is 1.86 .

Given that the variance of the score on one spin of this spinner is also 1.2 , test Johann's suspicion at the 5\% significance level.

All question bank results loaded