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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