In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. $$\begin{array} { | l | r | r | r | r | r | }
\hline \text { Meals } & 0 & 1 & 2 & 3 & \geq 4 \
\hline \text { Observed frequency } & 287 & 581 & 447 & 290 & 185 \
\hline
\end{array}$$ Using$\alpha$=0.05, the appropriate decision for this goodness of fit test is _______.

Question

In a college dining hall, students with a full meal plan can eat up to four meals each day.The kitchen would like to know the distribution of meal consumption by students and think it would follow a Poisson distribution.Reviewing dining hall data over the past week, the following information is compiled. $$\begin{array} { | l | r | r | r | r | r | } 
\hline \text { Meals } & 0 & 1 & 2 & 3 & \geq 4 \
\hline \text { Observed frequency } & 287 & 581 & 447 & 290 & 185 \
\hline
\end{array}$$ Using$\alpha$=0.05, the appropriate decision for this goodness of fit test is _______.

Quizplus · Accepted Answer

Without the actual calculations of the expected frequencies and the chi-square test value, it's not possible to definitively conclude the correct decision based on the information provided. However, the question seems to imply that a goodness of fit test was conducted to compare the observed frequencies of meal consumption to the expected frequencies under a Poisson distribution. The decision to reject or not reject the null hypothesis would be based on the comparison of the calculated chi-square statistic to the critical value from the chi-square distribution table at the given significance level (α=0.05). Since we cannot calculate the expected frequencies or the chi-square statistic without the Poisson distribution's mean (λ), and since the question does not provide a direct outcome of the test, any choice made here would be speculative. However, the correct procedure involves calculating these values and making a decision based on the comparison, typically leading to either rejecting the null hypothesis if the observed distribution significantly differs from the expected Poisson distribution, or not rejecting it if they do not significantly differ.

In a College Dining Hall, Students with a Full Meal