Compare two Poisson means

A question is this type if and only if it requires testing whether two independent Poisson means are different, typically using normal approximation for the difference.

2 questions · Standard +0.6

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AQA S3 2010 June Q3
7 marks Standard +0.8
3
The weekly number of hits, \(S\), on Sam's website may be modelled by a Poisson distribution with parameter \(\lambda _ { S }\). The weekly number of hits, \(T\), on Tina's website may be modelled by a Poisson distribution with parameter \(\lambda _ { T }\).
During a period of 40 weeks, the number of hits on Sam's website was 940.
During a period of 60 weeks, the number of hits on Tina's website was 1560.
Assuming that \(S\) and \(T\) are independent random variables, investigate, at the \(2 \%\) level of significance, Tina's claim that the mean weekly number of hits on her website is greater than that on Sam's website.
(7 marks)

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AQA S3 2016 June Q3
7 marks Standard +0.3
Car parking in a market town's high street was, until 31 May 2014, limited to one hour free of charge between 8 am and 6 pm. Records show that, during a period of 30 days prior to this date, a total of 315 penalty tickets were issued. Car parking in the high street later became limited to thirty minutes free of charge between 8 am and 6 pm. A subsequent investigation revealed that, during a period of 60 days from 1 October 2014, a total of 747 penalty tickets were issued. The daily numbers of penalty tickets issued may be modelled by independent Poisson distributions with means \(\lambda_A\) until 31 May 2014 and \(\lambda_B\) from 1 October 2014. Investigate, at the 1\% level of significance, a claim by traders on the high street that \(\lambda_B > \lambda_A\). [7 marks]