Moderate -0.3 This is a standard one-sample z-test for a mean with all parameters given explicitly. Students must state hypotheses, calculate a test statistic using the normal distribution (ฯ known, n=30), compare to critical value at 2.5% level, and conclude. It's routine A-level statistics requiring no problem-solving insight, though the multi-step procedure and correct interpretation prevent it from being trivial.
The number of working hours per week of employees in a company is modelled by a normal distribution with mean of 34 hours and a standard deviation of 4.5 hours.
The manager claims that the mean working hours per week of the company's employees has increased.
A random sample of 30 employees in the company was found to have mean working hours per week of 36.2 hours.
Carry out a hypothesis test at the 2.5% significance level to investigate the manager's claim.
[6 marks]
Question 17:
17 | States both hypotheses
correctly for one-tailed test | 2.5 | B1 | X = working hours per week
๐ป๐ป0:๐๐ = 34
๐ป๐ป2 1:๐๐ > 34
4.5
xฬ ~ N(34, )
30
P(xฬ > 36.2) = 0.004
0.004 < 0.025
Reject
There i๐ป๐ปs 0 sufficient evidence to
suggest that the mean working
hours have increased.
States or uses correct model
PI by mean 34 and
4.52
variance or
30
4.5
standard deviation OE
30
or by correct probability AWFW
[0.0037, 0.004]
36.2โ34
or test statistic ยฑ
4.5รท 30
or test statistic value
AWFW ยฑ[2.67, 2.68]
or critical
region > AWFW [35.6, 35.632]
condone โฅ
or critical value [35.6, 35.632] | 1.1a | M1
ยฑ
Obtains AWFW
[0.0037, 0.004]
or
obtains the correct value of the
test statistic AWFW [2.67, 2.68]
or
obtains the correct critical
region > AWFW [35.6, 35.632]
condone โฅ
condone incorrect missing or
incorrect labels | 1.1b | A1
Compares their [0.0037, 0.004]
with 0.025
or
compares their [2.67, 2.68]
with 1.96
allow positive values up to 4 for
1.96
or
compares their region
> [35.6, 35.632] with 36.2
condone โฅ | 3.5a | M1
Infers H or null hypothesis
0
rejected
Condone or alternative
hypothesis accepted
All figures ๐ป๐ปm 1 ust be correct | 2.2b | A1
Concludes correctly in context
that there is sufficient
evidence to suggest that the
mean working hours have
increased
To be awarded R1, marks
M1A1M1A1 must be scored as
the minimum | 3.2a | R1
Question 17 Total | 6
Q | Marking instructions | AO | Marks | Typical solution
The number of working hours per week of employees in a company is modelled by a normal distribution with mean of 34 hours and a standard deviation of 4.5 hours.
The manager claims that the mean working hours per week of the company's employees has increased.
A random sample of 30 employees in the company was found to have mean working hours per week of 36.2 hours.
Carry out a hypothesis test at the 2.5% significance level to investigate the manager's claim.
[6 marks]
\hfill \mbox{\textit{AQA Paper 3 2022 Q17 [6]}}