Harry has a five-sided spinner with sectors coloured blue, green, red, yellow and black. Harry thinks the spinner may be biased. He plans to carry out a hypothesis test with the following hypotheses. Ho: P(the spinner lands on blue) = }1/5 H₁: P(the spinner lands on blue) ≠ 3 Harry spins the spinner 300 times. It lands on blue on 45 spins. Use a suitable approximation to carry out Harry's test at the 5% significance level.

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2022). The mark or mark type is shown in brackets.

1. [B1] B(300, 1/5) → N(60,48) SOI
2. [M1] Condone with wrong or no continuity correction
3. [A1] = -2.093
4. [M1] Valid comparison '2.093' > 1.96 Note: $(`-2.093`) (= 0.0182), 0.0182 < 0.025
5. [A1 FT] [Evidence to reject Ho] There is evidence that P(landing on blue) ≠ 1/5 Allow ‘There is evidence that the spinner is biased.' In context, not definite, no contradictions Condone critical values method (critical value 46.42 M1 A1 and 45.5 < ‘46.42' M1 for valid comparison A1 for correct conclusion) SC: 0.0182 unsupported: 0.0182 < 0.025 And there is evidence that the spinner is biased. In context, not definite B1 only