Standard +0.3 This is a standard one-tailed hypothesis test for a proportion with clearly stated hypotheses (H₀: p=0.62, H₁: p>0.62). Students must check conditions for normal approximation, calculate the test statistic z = (p̂-p₀)/√(p₀(1-p₀)/n), and compare to the critical value at 1% significance. While it requires multiple steps and careful reasoning, it follows a routine procedure taught explicitly in AS statistics with no novel problem-solving required, making it slightly easier than average.
In this question you must show detailed reasoning.
Research showed that in May 2017 62% of adults over 65 years of age in the UK used a certain online social media platform. Later in 2017 it was believed that this proportion had increased. In December 2017 a random sample of 59 adults over 65 years of age in the UK was collected. It was found that 46 of the 59 adults used this online social media platform.
Use a suitable hypothesis test to determine whether there is evidence at the 1% level to suggest that the proportion of adults over 65 in the UK who used this online social media platform had increased from May 2017 to December 2017. [7]
Question 9:
9 | H : p = 0.62
0
H : p > 0.62
1
p is the proportion of adults over 65 in the (UK
population) who use the onine social media
platform
1 ‒ P(X ≤ 45) = 0.0068(1)
0.0068 < 0.01
Result is significant or “reject H ”
0
The evidence suggests that the proportion of
adults over 65 (in the UK population) using
platform has increased
from 62% | B1
B1
B1$
B1&
M1&
A1
E1
[7] | 1.1
1.1
2.5
1.1
1.1
2.2b
2.4 | Allow null
Allow alternative
May be seen in hypotheses
Allow probability
NB from use of B(59, 0.62)
Comparison of their 0.0068 with
0.01 or 0.68% with 1%; not allowed
from point probability
Depends on B1&M1&
Conclusion in context
Depends on all other marks
except B1$ | Allow for sight of 0.9932,
(from 0.99318902)
Allow ‘accept H ’
1
OR Critical region ≥ 46 B1
46 in critical region, M1,
hence conclusion
In this question you must show detailed reasoning.
Research showed that in May 2017 62% of adults over 65 years of age in the UK used a certain online social media platform. Later in 2017 it was believed that this proportion had increased. In December 2017 a random sample of 59 adults over 65 years of age in the UK was collected. It was found that 46 of the 59 adults used this online social media platform.
Use a suitable hypothesis test to determine whether there is evidence at the 1% level to suggest that the proportion of adults over 65 in the UK who used this online social media platform had increased from May 2017 to December 2017. [7]
\hfill \mbox{\textit{OCR MEI AS Paper 2 2018 Q9 [7]}}