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. $$\begin{array} { | l | l | l | l | l | l | l | }
\hline \text { Cars per 15-rrirute iriterval } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed frequency } & 5 & 15&17 & 12& 10 & 8 \
\hline
\end{array}$$

Using $\alpha$= 0.05, the appropriate decision 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. $$\begin{array} { | l | l | l | l | l | l | l | } 
\hline \text { Cars per 15-rrirute iriterval } & 0 & 1 & 2 & 3 & 4 & \geq 5 \
\hline \text { Observed frequency } &  5 & 15&17 & 12& 10 & 8 \
\hline
\end{array}$$

Using $\alpha$= 0.05, the appropriate decision for this goodness-of-fit test is ____.

Quizplus · Accepted Answer

To determine if the observed distribution fits a Poisson distribution, a goodness-of-fit test is used. Without the exact calculations (e.g., chi-square statistic, degrees of freedom), the decision cannot be definitively stated. However, the typical approach is to compare the observed frequencies with the expected frequencies under a Poisson distribution. If the differences are not statistically significant (based on the chi-square statistic and the critical value for $\alpha = 0.05$), we do not reject the null hypothesis, which in this context is that the observed distribution follows a Poisson distribution.

Sami Schmitt Believes That the Number of Cars Arriving at His