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 critical value of chi-square 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 critical value of chi-square for this goodness of fit test is _______.

Quizplus · Accepted Answer

The degrees of freedom for this test is the number of categories minus 1, which is 4 (since there are 5 categories: 0, 1, 2, 3, ≥4). Using a chi-square distribution table with 4 degrees of freedom and a significance level of 0.05, the critical value is 7.81.

In a College Dining Hall, Students with a Full Meal