A bank runs a campaign to promote Internet banking accounts to their customers - AQA - A-Level Maths Pure - Question 19 - 2022 - Paper 3
Question 19
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 we... show full transcript
Worked Solution & Example Answer:A bank runs a campaign to promote Internet banking accounts to their customers - AQA - A-Level Maths Pure - Question 19 - 2022 - Paper 3
Step 1
State the hypotheses
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Answer
Let ( p ) represent the proportion of customers with an Internet banking account after the campaign.
Null Hypothesis, ( H_0: p = 0.42 )
Alternative Hypothesis, ( H_1: p > 0.42 )
Step 2
Determine the sample proportion and use the binomial distribution
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Answer
The number of customers surveyed is ( n = 35 ), and the number who registered is ( X = 18 ).
The sample proportion is ( \hat{p} = \frac{18}{35} \approx 0.5143 ).
We will examine the critical values under the null hypothesis using the binomial distribution.
Step 3
Calculate the probability
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Using the binomial formula, we calculate:
( P(X \leq 18) ) using the binomial distribution ( B(n = 35, p = 0.42) ).
From tables or software, we find ( P(X \leq 18) \approx 0.168 ).
Thus, the critical value for a one-tailed test at a 10% significance level would be at 19.
Step 4
Evaluate the results
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Since ( P(X \leq 18) \approx 0.168 ) which is greater than 0.10, we fail to reject the null hypothesis. This indicates insufficient evidence to suggest an increase in the proportion of customers registered for an Internet banking account.
Step 5
Conclusion
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In conclusion, after conducting the hypothesis test, there is not enough statistical evidence to support the claim that the proportion of customers with Internet banking accounts has increased since the campaign.
