Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. $$\begin{array} { | l | l | l | l | l | l | l | }
\hline \text { Categary } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed } & 5 & 15&17 & 12& 10 & 8 \
\hline
\end{array}$$
The number of degrees of freedom for this goodness-of-fit test is _______.

Question

Sami Schmitt believes that the number of cars arriving at his Scrub and Shine Car Wash follows a Poisson distribution.He collected a random sample and constructed the following frequency distribution to test his hypothesis. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Categary } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed } &  5 & 15&17 & 12& 10 & 8 \
\hline
\end{array}$$
 The number of degrees of freedom for this goodness-of-fit test is _______.

Quizplus · Accepted Answer

The degrees of freedom for a goodness-of-fit test are calculated as the number of categories minus one. Since there are 6 categories (0, 1, 2, 3, 4, ≥5), the degrees of freedom are 6 - 1 = 5. However, because the Poisson distribution is being tested, and it has a parameter (the mean rate, λ), we must adjust the degrees of freedom by subtracting the number of estimated parameters. In this case, we estimate one parameter (λ), so the degrees of freedom are 5 - 1 = 4.

Sami Schmitt Believes That the Number of Cars Arriving at His