A-LevelMathematicsProbability and statistics9709/62 · Feb/Mar 2022 · Q46 Marks

In the past the time, in minutes, taken by students to complete a certain challenge had mean 25.5 and standard deviation 5.2. A new challenge is devised and it is expected that students will take, on average, less than 25.5 minutes to complete this challenge. A random sample of 40 students is chosen and their mean time for the new challenge is found to be 23.7 minutes.

(a)Assuming that the standard deviation of the time for the new challenge is 5.2 minutes, test at the 1% significance level whether the population mean time for the new challenge is less than 25.5 minutes.[5]
(b)State, with a reason, whether it is possible that a Type I error was made in the test in part (a).[1]

Mark scheme

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

[B1] Ηο: μ = 25.5 Η₁: μ < 25.5
[M1] 23.7-25.5 / 5.2÷√40 Must have √40
[A1] = -2.189
[M1] For valid comparison '2.189' <2.326 For two-tailed test: allow compare 2.576 if H₁: μ ≠ 25.5
[A1 FT] [Accept Ho] No evidence that mean time has decreased In context, not definite, no contradictions FT their 2.189 but no FT for two-tailed test N.B. Use of two-tailed test can score max B0 M1 A1 M1 A0 Condone use of critical value method (23.59 M1 A1 and 23.7 > 23.59 M1 A1 correct conclusion or 25.612 M1 A1 and 25.5 < 25.612 M1 A1 with correct conclusion)
[B1 FT] No, because Ho was not rejected FT their conclusion in (a)

On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.