# Description of a Goodness of Fit Test

Scenario: Banner Mattress and Furniture Company wishes to study the number of credit applications received per day for the last 300 days. The information is reported as follows:

Number of credit applications Frequency (Number of days)

0 50

1 77

2 81

3 48

4 31

5 13

To interpret, there were 50 days on which no credit applications were received. 77 days on which only one application was received, and so on. Therefore, would it be reasonable to conclude that the population distribution is Poisson with a mean of 2.0? Use the .05 significance level.

Hint: To find the expected frequencies use the Poisson distribution with a mean of 2.0. Find the probability of exactly one success given a Poisson distribution with a mean of 2.0. Multiply this probability by 300 to find the expected frequency for the number of days in which there was exactly one application. Determine the expected frequency for the other days in a similar manner.

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#### Solution Preview

Please refer to the attached file for better clarity of the table and missing expressions.

Poisson Expected Frequency Observed Frequency

Number of applications Probability Fe=300*P Fo (Fo-Fe)^2 (Fo-Fe)^2/Fe

P

0 0.1353 40.60 50 ...

#### Solution Summary

This solution illustrates how to determine if the given population follows a Poisson distribution. An attached Excel document is provided which includes all the required formulas and calculations.