The probability of a biased die landing on 6 is 0.4. Polly suspects that the probability of the die landing on 6 is not 0.4.
The die was rolled 20 times and landed on 6 eleven times.
The critical region for a two-tailed test of Polly's suspicion is X≤3 X \leq 3\,X≤3 and X≥13X \geq 13X≥13.
Comment on Polly's suspicion in light of the experiment
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.