The time, in minutes, spent by customers at a particular gym has the distribution N(μ, 38.2). In the past the value of μ has been 42.4. Following the installation of some new equipment the management wishes to test whether the value of μ has changed.

Mark scheme

Marking points from the official mark scheme (May/June 2021). The mark or mark type is shown in brackets.

1. [B1] (a) Conclude that (population) mean time has changed (or is not 42.4) although μ has not changed (or is still 42.4); OE. In context.
2. [B1] (b) Ho: population mean (or μ) = 42.4; H1: population mean (or μ) ≠ 42.4; Not just 'mean'. (could be seen in (a))
3. [M1] (b) (45.6-42.4) / √(38.2/20); For standardising (must have √20)
4. [A1] (b) ± 2.315
5. [M1] (b) 2.240 < '2.315'; For valid comparison (accept 2.241) or P(z > 2.315) = 0.0103 < 0.0125 oe
6. [A1 FT] (b) There is evidence that μ or mean time has changed; FT their z; In context, not definite. No contradictions. Note: Accept correct alternative methods SC: One tail test no FT. Can score B0 M1 A1 M1 (comparison with 1.96) A0 (maximum 3 out of 5)