Standard +0.3 This is a standard A-level hypothesis test using the binomial distribution with clearly stated hypotheses, significance level, and context. It requires routine application of the binomial test procedure (finding P(X ≥ 18), comparing to 10% level, and stating conclusion) but involves no conceptual challenges beyond textbook examples. The 6 marks reflect the method marks for a complete solution rather than inherent difficulty.
A bank runs a campaign to promote Internet banking accounts to their customers.
Before the campaign, 42% of their customers had an Internet banking account.
One week after the campaign started, 35 customers were surveyed at random and 18 of them were found to have registered for an Internet banking account.
Using a binomial distribution, carry out a hypothesis test at the 10% significance level to investigate the claim that, since the campaign, there has been an increase in the proportion of customers registered for an Internet banking account.
[6 marks]
Question 19:
19 | States both hypotheses
correctly for one-tailed test
0.42 OE | 2.5 | B1 | X = number of customers with an
internet banking account
: p = 0.42
: p > 0.42
𝐻𝐻0
𝐻𝐻U 1 nder null hypothesis
X B(35,0.42)
P( ∼X ≥ 18) = 0.169
0.169 > 0.10
Do not reject
There is insuf𝐻𝐻fic 0 ient evidence to
suggest an increase in the
proportion of bank customers
registered for an internet banking
account.
States or uses correct model
PI by calculation of one of the
probabilities below
P(X ≤ 16) = [0.73, 0.733]
P(X ≤ 17) = [0.83, 0.832]
P(X ≤ 18) = [0.90, 0.903]
P(X ≥ 18) = [0.168, 0.17]
P(X ≥ 19) = [0.097, 0.10]
or critical value of 19 or region
≥ 19 | 3.3 | M1
Obtains P(X ≥ 18) =[0.168, 0.17]
or
Obtains a critical value 19 or
critical region ≥19 | 1.1b | A1
Evaluates binomial model by
comparing their P(X ≥ 18) with
0.10
or
Evaluates binomial model by
comparing their critical region
with 18 | 3.5a | M1
Infers H or null hypothesis not
0
rejected
Condone H accepted
0
or or alternative hypothesis
rejected
All 𝐻𝐻fi 1 gures must be correct | 2.2b | A1
Concludes correctly in context
that there is insufficient
evidence to suggest an
increase in the proportion of
bank customers registered for
an internet banking account
To be awarded R1, marks
M1A1M1A1 must be scored as
the minimum | 3.2a | R1
Question 19 Total | 6
Question Paper Total | 100
A bank runs a campaign to promote Internet banking accounts to their customers.
Before the campaign, 42% of their customers had an Internet banking account.
One week after the campaign started, 35 customers were surveyed at random and 18 of them were found to have registered for an Internet banking account.
Using a binomial distribution, carry out a hypothesis test at the 10% significance level to investigate the claim that, since the campaign, there has been an increase in the proportion of customers registered for an Internet banking account.
[6 marks]
\hfill \mbox{\textit{AQA Paper 3 2022 Q19 [6]}}