The number of calls arriving at a switchboard from noon to 1 PM during the business days Monday through Friday is monitored for six weeks (i. e., 30 days). Let X be defined as the number of calls during that one-hour period. The relative frequency of calls was recorded and reported as Value 5 68 9 10
Relative Frequency 0.067 0.067 0.100 0.133 0.200
Value 11 12 13 14 15
Relative
Frequency 0.133 0.133 0.067 0.033 0.067
(a) Does the assumption of a Poisson distribution seem appropriate as a probability model for this data? Use a = 0.05.
(b) Calculate the P-value for this test.

A) The assumption of a Poisson distribution is appropriate and we will fail to reject the null hypothesis since the critical value is lower than the level of significance

b) p-value = 0.834

Step-by-step explanation:

a) let the number of calls per hour = X

number of sample points = 10

the expected number of calls per hour : E (x)

= ∑ xi * yi  = 10.221

given boundaries are : n - 1 , i = 0

Therefore the mean ( β ) number of calls per hour = 10.221

Note : The interesting event is the number of calls that arrives per hour

applying hypothesis testing :

H0 :   α ≤ β  ( null hypothesis )

Ha :   α ≥ β  ( alternate hypothesis )

we will fail to reject the null hypothesis since the critical value is lower than the level of significance

attached below is the remaining part of the solution

b) P-value = 0.834

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