CAIE A-Level Mathematics 6.5.4 Hypothesis tests

Practise interpreting Type I and Type II errors from the test decision, including when each error is possible or impossible.

Exam points

explain a Type I error as rejecting H0 when the original claim is actually true
decide whether Type I or Type II errors are possible from whether H0 was rejected
state the Type I error probability from the significance level or rejection region

[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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6.5.4—Hypothesis tests question 1