CAIE S2 2018 June — Question 7

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2018
SessionJune
TopicHypothesis test of binomial distributions
TypePerform one-tailed hypothesis test

7 A ten-sided spinner has edges numbered \(1,2,3,4,5,6,7,8,9,10\). Sanjeev claims that the spinner is biased so that it lands on the 10 more often than it would if it were unbiased. In an experiment, the spinner landed on the 10 in 3 out of 9 spins.
  1. Test at the \(1 \%\) significance level whether Sanjeev's claim is justified.
  2. Explain why a Type I error cannot have been made.
    In fact the spinner is biased so that the probability that it will land on the 10 on any spin is 0.5 .
  3. Another test at the \(1 \%\) significance level, also based on 9 spins, is carried out. Calculate the probability of a Type II error.
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.