Polly suspects that a die is biased. The probability of the die landing on 6 is believed to be 0.4, and Polly thinks this probability has changed. The die is to be rolled 20 times, and X X\,X is the number of sixes obtained.
Write down the hypotheses Polly should use.
Using a 10% significance level, find the critical region for a two-tailed test, with a probability of at most 0.05 in each tail.
Find the actual significance level of a test based on this critical region.
Polly rolls the die 20 times and obtains 11 sixes. Comment on Polly's suspicion.
316 exam-style questions on OCR A Level Maths 2.5 Statistical Hypothesis Testing, covering 2.5.1 The language of hypothesis testing, 2.5.2 Hypothesis test for a binomial proportion, 2.5.3 Inference and significance level, 2.5.4 Sample mean as a random variable (A-level only), 2.5.5 Hypothesis test for the mean of a normal distribution (A-level only), 2.5.6 Pearson's product-moment correlation coefficient, and 2.5.7 Hypothesis test using Pearson's coefficient (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.