CAIE A-Level Mathematics A2 6.5.4 Hypothesis Tests Questions

Practise interpreting Type I and Type II errors and their probabilities in hypothesis tests.

Exam points

define Type I and Type II errors in context
determine the probability of a Type I error from the significance level
explain when Type II errors are possible or impossible

[Maximum number: 2]

At a certain large school it was found that the proportion of students not wearing correct uniform was 0.15 . The school sent a letter to parents asking them to ensure that their children wear the correct uniform. The school now wishes to test whether the proportion not wearing correct uniform has been reduced.

State, with a reason, which of the errors, Type I or Type II, may have been made.

$Not rejected \mathrm{H}_0 *B1 FT FT If Reject \mathrm{H}_0 in (d) Type II DB1 FT FT Type I$

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CAIE A-Level Mathematics A2 6.5.4 Hypothesis Tests Questions question 1