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

Quizplus · Accepted Answer

The appropriate decision for this goodness-of-fit test is to not reject the null hypothesis that the observed distribution is Poisson. This conclusion is reached by comparing the calculated chi-square statistic (3.889) with the critical value of the chi-square distribution (9.488) for 8 degrees of freedom at a significance level of 0.05. Since the calculated chi-square value is less than the critical value, we cannot reject the null hypothesis and conclude that the observed distribution is not significantly different from a Poisson distribution.

Sami Schmitt Believes That Number of Cars Arriving at His α\alphaα

Sami Schmitt Believes That Number of Cars Arriving at His $\alpha$