Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. The number of degrees of freedom for this goodness-of-fit test is _______.

Question

Sami Schmitt believes that number of cars arriving at his Scrub and Shine Car Wash follow a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis.  The number of degrees of freedom for this goodness-of-fit test is _______.

Quizplus · Accepted Answer

The number of degrees of freedom for a goodness-of-fit test is (number of categories - 1), which in this case is (6-1) = 5. However, since the Poisson distribution has only one parameter (the mean), the expected counts for each category can be calculated from the sample mean alone. This means that one degree of freedom is lost, giving a final degree of freedom of 4.

Sami Schmitt Believes That Number of Cars Arriving at His