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. A suitable sample of 50 students is selected and the number not wearing correct uniform is noted. This figure is used to carry out a test at the $$$5 \%$$$ significance level. In fact 4 students out of the 50 are not wearing correct uniform. State the conclusion of the test, explaining your answer. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_61 Year：2021 Question No：8(d)

Answer:

4 is outside critical region $(\leqslant 3)$ OE or $\mathrm{P}(X \leqslant 4)=0.112$ which is $>0.05$
No evidence that proportion not wearing the correct uniform has decreased (Accept Ho)

Knowledge points:

6.5.1 understand the nature of a hypothesis test, the difference between one-tailed and two-tailed tests, and the terms null hypothesis, alternative hypothesis, significance level, rejection region (or critical region), acceptance region and test statistic (Outcomes of hypothesis tests are expected to be interpreted in terms of the contexts in which questions are set.)

Answer:

Knowledge points:

Solution:

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