Monica, a chef at a 5 -star restaurant, makes eight different desserts. She wants to see if the customers prefer any specific dessert over another. She keeps a record of desserts ordered over the course of several weeks. At $a = 0.05$, check to see if the desserts being ordered are equally distributed.
$\begin{array} { l l c } & \text { Dessert } & \text { Frequenc } \ & \text { Chocolate Mousse } & 25 \ & \text { Baked Alaska } & 12 \ & \text { Orange Cheesecake } & 23 \ & \text { Caramel Flan } & 32 \ & \text { Banana Brûlée } & 40 \ & \text { Mississippi Mud Pie } & 20 \ & \text { Ricotta Cannoli } & 38 \ \text { Table 11-2 } & \text { French Walnut Torte } & 34 \end{array}$
-What is the critical value?
A) 20.090
B) 13.362
C) 14.067
D) 15.507

Question

Quizplus · Accepted Answer

We can use the chi-square goodness of fit test with the following hypotheses:
$H_0$: The desserts are equally distributed
$H_1$: The desserts are not equally distributed

Using a chi-square calculator, we get a test statistic of 27.06. The degrees of freedom is 7 (number of desserts - 1). Looking at the chi-square distribution table with 7 degrees of freedom and a significance level of 0.05, the critical value is 14.067.

Since the test statistic (27.06) is greater than the critical value (14.067), we reject the null hypothesis and conclude that the desserts are not equally distributed. Therefore, some desserts are preferred over others.

Monica, a Chef at a 5 -Star Restaurant, Makes Eight a=0.05a = 0.05a=0.05

Monica, a Chef at a 5 -Star Restaurant, Makes Eight $a = 0.05$