Language of hypothesis testingEdexcel A-Level Maths: Mind map

Exam questions on Language of hypothesis testing

1. A coin is suspected of being biased towards heads. Let $p$ be the probability that the coin lands heads. The coin is tossed 20 times and $X$ is the number of heads. A hypothesis test is carried out at the 5% significance level.
   The critical region for this test is $X\ge15$. Find the actual probability of rejecting $H_0$ when it is true.2 marks
2. A die is thought to be biased with respect to sixes. Let $p$ be the probability that the die lands on six. The die is rolled 30 times and $X$ is the number of sixes. The test of $H_0:p=\frac16$ against $H_1:p\ne\frac16$ is carried out at the 10% significance level.
   Find the critical region for the lower tail of this test.2 marks
3. A manufacturer claims that 20% of its chocolate eggs contain a toy. A child believes that the proportion is greater than 20%. In a random sample of 25 eggs, 9 contain a toy. Let $p$ be the proportion of all the manufacturer's eggs that contain a toy, and let $X$ be the number of eggs in a sample of 25 that contain a toy.
   State the null and alternative hypotheses, and state the distribution of $X$ if the null hypothesis is true.3 marks