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

The observed value of chi-square for this goodness-of-fit test is closest to _____.

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

The observed value of chi-square for this goodness-of-fit test is closest to _____.

Quizplus · Accepted Answer

The chi-square statistic is calculated as the sum of the squared differences between the observed and expected frequencies, divided by the expected frequencies. The expected frequencies are calculated under the assumption that the Poisson distribution is a good fit for the data. In this case, the expected frequencies are:0: 4.41: 8.82: 113: 114: 9.2>=5: 5.6The chi-square statistic is then calculated as:(5-4.4)^2/4.4 + (15-8.8)^2/8.8 + (17-11)^2/11 + (12-11)^2/11 + (10-9.2)^2/9.2 + (8-5.6)^2/5.6 = 0.73Therefore, the observed value of chi-square for this goodness-of-fit test is closest to 0.73.

Sami Schmitt Believes That the Number of Cars Arriving at His