Test with normal approximation

A question is this type if and only if it requires using a normal approximation to the Poisson distribution to carry out a hypothesis test, typically for large λ or long time periods.

3 questions · Standard +0.3

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CAIE S2 2011 June Q5
9 marks Standard +0.3
The number of adult customers arriving in a shop during a 5-minute period is modelled by a random variable with distribution \(\text{Po}(6)\). The number of child customers arriving in the same shop during a 10-minute period is modelled by an independent random variable with distribution \(\text{Po}(4.5)\).
  1. Find the probability that during a randomly chosen 2-minute period, the total number of adult and child customers who arrive in the shop is less than 3. [3]
  2. During a sale, the manager claims that more adult customers are arriving than usual. In a randomly selected 30-minute period during the sale, 49 adult customers arrive. Test the manager's claim at the 2.5\% significance level. [6]
Edexcel S2 2009 January Q6
14 marks Standard +0.3
A web server is visited on weekdays, at a rate of 7 visits per minute. In a random one minute on a Saturday the web server is visited 10 times.
    1. Test, at the 10\% level of significance, whether or not there is evidence that the rate of visits is greater on a Saturday than on weekdays. State your hypotheses clearly.
    2. State the minimum number of visits required to obtain a significant result.
    [7]
  2. State an assumption that has been made about the visits to the server. [1]
In a random two minute period on a Saturday the web server is visited 20 times.
  1. Using a suitable approximation, test at the 10\% level of significance, whether or not the rate of visits is greater on a Saturday. [6]
OCR S2 2010 January Q5
8 marks Standard +0.3
The number of customers arriving at a store between 8.50 am and 9 am on Saturday mornings is a random variable which can be modelled by the distribution Po(11.0). Following a series of price cuts, on one particular Saturday morning 19 customers arrive between 8.50 am and 9 am. The store's management claims, first, that the mean number of customers has increased, and second, that this is due to the price cuts.
  1. Test the first part of the claim, at the 5% significance level. [7]
  2. Comment on the second part of the claim. [1]