The chance of getting a 3 on a fair spinner is 14\displaystyle \frac{1}{4}41. The spinner is spun 12 times.
The probability that the spinner lands on 3 exactly r r\,r times is 0.232. Find rrr.
The probability that the spinner lands on 3 more than r r\,r times is 0.1576. Find rrr.
Alex believes that the spinner is not fair and the chance of the spinner landing on 3 is greater than 14\displaystyle \frac{1}{4}41. To test this claim she spins the spinner 40 times. The probability of obtaining a result at least as large as the number of times the spinner lands on 3 is 0.0544. Stating your hypotheses clearly, find the number of times the spinner lands on 3 and state whether there is enough evidence to support Alex's claim at the 5% significance level.
153 exam-style questions on Edexcel A Level Maths Hypothesis Testing, covering 7.1 Hypothesis Testing, 7.2 Finding Critical Values, 7.3 One-Tailed Tests, and 7.4 Two-Tailed Tests. Each one has a worked solution and a mark scheme showing where the marks go.