Moderate -0.3 This is a standard hypothesis test for a proportion with clearly stated hypotheses (H₀: p=0.15, H₁: p≠0.15). Students must check validity (np=7.5, n(1-p)=42.5 both >5), calculate the test statistic using normal approximation, and compare to critical values. While it requires multiple steps and proper statistical reasoning, it follows a routine procedure taught explicitly in AS statistics with no novel problem-solving required. Slightly easier than average due to straightforward setup and clear context.
It is known from historical data that 15% of the residents of a town buy the local weekly newspaper, 'Local News'.
A new free weekly paper is introduced into the town.
The owners of 'Local News' are interested to know whether the introduction of the free newspaper has changed the proportion of residents who buy their paper.
In a random sample of 50 residents of the town taken after the free newspaper was introduced, it was found that 3 of them purchased 'Local News' regularly.
Investigate, at the 5% significance level, whether this sample provides evidence that the proportion of local residents who buy 'Local News' has changed.
[6 marks]
Question 19:
19 | States both hypotheses correctly for
a two-tailed test. Accept population
proportion for p. Accept 15%, but
not ‘x =’ or ‘ =’ or ‘µ =’ | 2.5 | B1 | X is ‘Number of residents who buy
Local News’
H : p = 0.15
0
H : p ≠ 0.15
1
Under H : X ~ B(50 , 0.15)
0
P(X ≤ 3) = 0.04604657
As 0.046 > 0.025
Accept H
0
There is insufficient evidence to
suggest that the proportion of
residents buying ‘Local News’ has
changed.
States model 𝑑𝑑used (PI by 0.046,
0.032, 0.014, 0.112) (AWRT) | 1.1a | M1
Evaluates P(X ≤ 3) = 0.046 (PI)
(condone 0.014 for A1) | 1.1b | A1
Compares 0.046 or 0.014 with
0.025.
Must see clear comparison
(inequality or diagram) | 3.5a | M1
Infers H is not rejected
0
(PI)(CSO)(OE) | 2.2b | A1
Concludes correctly in context CSO
‘insufficient evidence’ OE required.
Only award for full complete correct
solution. | 3.2a | R1
Total | 6
It is known from historical data that 15% of the residents of a town buy the local weekly newspaper, 'Local News'.
A new free weekly paper is introduced into the town.
The owners of 'Local News' are interested to know whether the introduction of the free newspaper has changed the proportion of residents who buy their paper.
In a random sample of 50 residents of the town taken after the free newspaper was introduced, it was found that 3 of them purchased 'Local News' regularly.
Investigate, at the 5% significance level, whether this sample provides evidence that the proportion of local residents who buy 'Local News' has changed.
[6 marks]
\hfill \mbox{\textit{AQA AS Paper 2 2020 Q19 [6]}}