A survey carried out in a town in 2020 found that 30% of adults regularly cycled to work. Since then a network of cycle lanes has opened in the town. A council officer believes that the proportion of adults in the town who regularly cycle to work has changed. To investigate, she asks 25 adults leaving the town's leisure centre one Saturday morning whether they regularly cycle to work, and uses X, the number who say yes, to carry out a hypothesis test.
(a) Explain why the officer should use a two-tailed test. (1 mark)
(b) Stating your hypotheses clearly, determine the critical region for the test at the 5% significance level, showing the probabilities you use. Find the actual significance level of the test. (5 marks)
(c) In fact 12 of the 25 adults say that they regularly cycle to work. State, with a reason, the conclusion of the test in context. (2 marks)
(d) Explain why the way the officer chose her sample makes the conclusion of the test unreliable. (1 mark) ●●●●●Level 49 marksStart→