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. Use a binomial distribution to find the probability of a Type I error. You must justify your answer fully. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................
Exam No：9709_s21_qp_61 Year：2021 Question No：8(c)
Answer:
Any two probs attempted using \(\mathrm{B}(50,0.15)\)
\(\mathrm{P}(X \leqslant 3)=0.85^{50}+50 \times 0.85^{49} \times 0.15+{ }^{50}
\mathrm{C}_{2} \times 0.85^{48} \times 0.15^{2}+{ }^{50} \mathrm{C}_{3} \times 0.85^{47} \times\) \(0.15^{3}\)
\(\mathrm{P}(X \leqslant 4)=0.04605+{ }^{50} \mathrm{C}_{4} \times 0.85^{46} \times 0.15^{4}\)
\(\mathrm{P}(X \leqslant 3)=0.0460\) or \(0.0461[<0.05]\)
\(\mathrm{P}(X \leqslant 4)=0.112\) or \([>0.05]\)
\(\mathrm{P}(\) Type I \()=0.0460\) or \(0.0461(3 \mathrm{sf})\)
\(\mathrm{P}(X \leqslant 3)=0.85^{50}+50 \times 0.85^{49} \times 0.15+{ }^{50}
\mathrm{C}_{2} \times 0.85^{48} \times 0.15^{2}+{ }^{50} \mathrm{C}_{3} \times 0.85^{47} \times\) \(0.15^{3}\)
\(\mathrm{P}(X \leqslant 4)=0.04605+{ }^{50} \mathrm{C}_{4} \times 0.85^{46} \times 0.15^{4}\)
\(\mathrm{P}(X \leqslant 3)=0.0460\) or \(0.0461[<0.05]\)
\(\mathrm{P}(X \leqslant 4)=0.112\) or \([>0.05]\)
\(\mathrm{P}(\) Type I \()=0.0460\) or \(0.0461(3 \mathrm{sf})\)
Knowledge points:
6.5.5 calculate the probabilities of making Type I and Type II errors in specific situations involving tests based on a normal distribution or direct evaluation of binomial or Poisson probabilities.
Solution:
Download APP for more features
1. Tons of answers.
2. Smarter Al tools enhance your learning journey.
IOS
Download
Download
Android
Download
Download
Google Play
Download
Download