Provide all calculations/explanation An aged care office has staffing concerns about the number of calls they receive. If the number ofcalls per 5-minute interval exceeds 2, then a new receptionist should be hired. Over a particular 1-hourtime interval, 29 calls were received.Assuming that the calls arrive in a Poisson distribution, conduct a hypothesis test with a 1%significance level to determine whether a new receptionist should be hired.

Name: Provide all calculations/explanation An aged care office has staffing
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Provide all calculations/explanation An aged care office has staffing concerns about the number of calls they receive. If the number ofcalls per 5-minute interval exceeds 2, then a new receptionist should be hired. Over a particular 1-hourtime interv

Poisson distribution: A random variable X is said to have a Poisson distribution with a parameter λ if its probability mass function (p.m.f) is as given below:Calculation: Denote the random variable X = Number of calls received. It is given that, over a particular 1-hour time interval, 29 calls were received. Here, it is given that, if the number of calls per 5-minute interval exceeds 2, then a new receptionist should be hired. In the given scenario, the parameter is λ = 5*(29/60) = 2.4167. Therefore, X ~ P(2.4167). The probability that the new receptionist should be hired is obtained as 0.4347 from the calculation given below: The level of significance is α = 0.01. Here, the probability that the new receptionist should be hired is (= 0.4347) is greater than 0.01. Since, the P-value is greater than the level of significance, we cannot reject the null hypothesis. Therefore, there is enough evidence to conclude that the new receptionist should be hired.