Hypothesis tests

Sample questions

Original practice questions written in the style of the exam.

1. Question 15 marks

   Before a new road layout was introduced, accidents at a junction occurred at a mean rate of 4 per month. In the two months after the layout was introduced there were 3 accidents.

   Test, at the 5% significance level, whether there is evidence that the mean rate of accidents has decreased. State your hypotheses clearly.

   [You may use $P(Y \le 3) = 0.0424$ for $Y \sim \text{Po}(8)$.]

   Mark scheme

   • B1 $H_0: \lambda = 8$, $H_1: \lambda < 8$ (per two months; or , per month) (1)
2. Question 26 marks

   A spinner is claimed to land on red with probability $0.25$. To test this claim the spinner is spun 40 times and the number of reds, $X$, is recorded. A two-tailed test is used at the 5% level, with the probability in each tail less than 0.025.

   For $X \sim B(40, 0.25)$:

   $c$