In the past, the mean time taken by Freda for a particular daily journey was 39.2 minutes. Following the introduction of a one-way system, Freda wishes to test whether the mean time for the journey has decreased. She notes the times, t minutes, for 40 randomly chosen journeys and summarises the results as follows. n = 40 Σt = 1504 Σt² = 57760

Mark scheme

Marking points from the official mark scheme (Feb/Mar 2020). The mark or mark type is shown in brackets.

1. [B1] est (µ) = 1504/40 = 37.6 or 188/5
2. [M1] est (σ²) = [1/(40-1)] * [57760 - (1504^2)/40]; Correct substitution in any correct formula [57760 - 1504^2/40]
3. [A1] = 31.(0) (3 sf); Accept 2016/65 or 31 1/65
4. [B1] H₀: Pop mean (or µ) = 39.2; H₁: Pop mean (or µ) < 39.2; Both. Not just 'mean'
5. [M1] ('37.6' - 39.2) / sqrt('31.0154' / 40); Allow use of biased variance (30.2), must have √40
6. [A1] = -1.817; SC FT use of biased = -1.840 for A1
7. [M1] '1.817' > 1.645 OE; Valid comparison 'their 1.817' with 1.645 or valid area comparison 0.0346 < 0.05 OE
8. [A1FT] There is evidence that mean time has decreased; FT their 1.817; in context, not definite, no contradictions; SC For 2 tail test: H₁: µ ≠ 39.2 and comp 1.96, max B0M1A1M1A0 (no FT for final mark)