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

Based on the given frequency distribution and using a goodness-of-fit test with a significance level of 0.05, we need to compare the expected values of the Poisson distribution with the observed frequencies. If the observed frequencies are not significantly different from the expected values, we fail to reject the null hypothesis that the distribution is Poisson. In this case, the calculated chi-square value is 5.49, which is less than the critical value of 9.488. Therefore, we do not reject the null hypothesis that the observed distribution is Poisson. Choice D is the correct answer.

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

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