Standard +0.3 This is a straightforward two-tailed hypothesis test for a population mean with known standard deviation. Students must calculate the sample mean (67.8), set up H₀: μ=65 vs H₁: μ≠65, find the test statistic z=(67.8-65)/(11.3/√100)≈2.48, compare to critical value (±2.326 at 2% level), and conclude. While it requires multiple steps and careful attention to the two-tailed nature and significance level, it follows a standard procedure taught extensively in A-level statistics with no novel problem-solving required.
A team game involves solving puzzles to escape from a room.
Using data from the past, the mean time to solve the puzzles and escape from one of these rooms is 65 minutes with a standard deviation of 11.3 minutes.
After recent changes to the puzzles in the room, it is claimed that the mean time to solve the puzzles and escape has changed.
To test this claim, a random sample of 100 teams is selected.
The total time to solve the puzzles and escape for the 100 teams is 6780 minutes.
Assuming that the times are normally distributed, test at the 2% level the claim that the mean time has changed.
[7 marks]
Question 15:
15 | States both hypotheses
correctly for two-tailed test
Accept population mean for | 2.5 | B1 | X = times to solve in minutes
𝐻𝐻 0: 𝜇𝜇 = 65
𝐻𝐻1: 𝜇𝜇 ≠ 65
= = 67.8
6780
𝑥𝑥
100
67.8 – 65
Test statistic =
11.3
�
√100
= 2.48
Critical value = 2.33
2.48 > 2.33
Reject
There is𝐻𝐻 0 sufficient evidence at the
2% level to suggest that mean
escape time has changed
Calculates mean of the sample
𝜇𝜇
PI in equation | 1.1b | B1
Formulates the test statistic or
uses the correct distribution of
their sample mean
PI by correct test statistic value
or calculates probability or
identifies acceptance region
Condone | 3.3 | M1
Obtains th6e5 c−or r6e7c.8t value of the
test statistic [2.47, 2.5]
or
obtains the correct probability
[0.0066, 0.007] or [0.0132,
0.014]
or
obtains the correct acceptance
region of [62.3, 67.7] | 1.1b | A1
Compares their value of test
statistic [2.47, 2.5] with their
critical value 2.33
Allow critical value [-4, 4] except
±0.02 or ±0.01
or
compares their probability
[0.0066, 0.007] with 0.01 or
compares their probability
[0.0132, 0.014] with 0.02
or
compares their sample mean
67.8 with their acceptance
region [62.3, 67.7] | 1.1b | M1
Compares correct values and
correctly infers is rejected
CSO
Allow reference𝐻𝐻 t 0 o | 2.2b | A1
Concludes correctly in context
that there is suffici e𝐻𝐻n 1 t
evidence to suggest that the
mean escape time has
changed
CSO | 3.2a | R1
Total | 7
≠ 6 | 5
Q | Marking Instructions | AO | Marks | Typical Solution
A team game involves solving puzzles to escape from a room.
Using data from the past, the mean time to solve the puzzles and escape from one of these rooms is 65 minutes with a standard deviation of 11.3 minutes.
After recent changes to the puzzles in the room, it is claimed that the mean time to solve the puzzles and escape has changed.
To test this claim, a random sample of 100 teams is selected.
The total time to solve the puzzles and escape for the 100 teams is 6780 minutes.
Assuming that the times are normally distributed, test at the 2% level the claim that the mean time has changed.
[7 marks]
\hfill \mbox{\textit{AQA Paper 3 2021 Q15 [7]}}