Originally Posted by

**bobby77** a chef at a 5-star restaurant makes 8 different desserts. She wants to see if the customers prefer any specific desert to another. She keeps a record of desserts ordered over the course of several weeks. At alpha=0.05, check to see if the desserts being ordered are equally distributed

Desserts Frequency

Chocolate Mousse 25

Baked Alaska 12

Orange Cheesecake 23

Caramel Flan 32

Banana Broulee 40

Mississippi Mud Pie 20

Ricotta Cannoli 38

French Walnut Torte 34

Find the critical value.

a. 20.090

b. 13.362

c. 14.067

d. 15.507

Here the null hypothesis H0 is that there is no difference in the frequencies

that deserts are ordered. Thus you have the table:

Code:

Desserts Observed Frequency Expected Freq under H0
Chocolate Mousse 25 28
Baked Alaska 12 28
Orange Cheesecake 23 28
Caramel Flan 32 28
Banana Broulee 40 28
Mississippi Mud Pie 20 28
Ricotta Cannoli 38 28
French Walnut Torte 34 28

You now need to perform a $\displaystyle \chi ^2$ test to compare the observed with the

expected frequencies with $\displaystyle \nu = 7$

The critical value of $\displaystyle \chi_{\nu=7} ^2$ to cut off $\displaystyle 95 \%$ is about 14.1, so the answer is c.

RonL