Suppose the number of calls arriving at an answering service during a given hour

Question

Suppose the number of calls arriving at an answering service during a given hour of the day is Poisson(lambda), where lambda elementof (0, infinity) is unknown. The number of calls actually received during this hour was recorded for 20 days and the following data were obtained. Construct an approximate 0.95-confidence interval for lambda. Assess the hypothesis that this is a sample from a Poisson(11) distribution. If you are going to decide that the hypothesis is false when the P-value is less than 0.05, then compute an approximate power for this procedure when lambda = 10.

Explanation / Answer

sample mean 'xbar' = 9.55

Sample standard deviation 's' = 3.017

T critical = 2.093

95% Confidence limits = [xbar ± T critical *s/n]

= [9.55 ± 2.093 *3.017/20]

= [8.138, 10.962]

power of the test = 1 - p[Accept H0/when it is false]

= 10.2%

approximately 10%

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