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

To test the hypothesis that the number of cars arriving at the car wash follows a Poisson distribution, we need to conduct a goodness-of-fit test. Looking at the frequency distribution table, we see that the expected frequencies are calculated by assuming a Poisson distribution with a mean of 8. Therefore, we can use the chi-square goodness-of-fit test to evaluate whether the observed frequencies fit this Poisson distribution. 
Using a significance level of 0.05, we compare the calculated chi-square test statistic (which measures the degree of discrepancy between the observed and expected frequencies) with the critical chi-square value at (8-1) degrees of freedom. In this case, we obtain a chi-square statistic of 3.89 and a critical chi-square value of 12.59. Since 3.89 < 12.59, we fail to reject the null hypothesis that the observed distribution is Poisson. Therefore, the appropriate decision is to do not reject the null hypothesis that the observed distribution is Poisson (choice D).

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

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