Question

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of $100$students and asks them, “Which type of food do you prefer: Ramen, tacos, pizza, or hamburgers?” Here are her data:

The chi-square test statistic is

a. $\frac{{(18-25)}^2}{25}+\frac{{(22-25)}^2}{25}+\frac{{(39-25)}^2}{25}+\frac{{(21-25)}^2}{25}$

b. $\frac{{(25-18)}^2}{18}+\frac{{(25-22)}^2}{22}+\frac{{(25-39)}^2}{39}+\frac{{(25-21)}^2}{21}$

c. $\frac{(18-25)}{25}+\frac{(22-25)}{25}+\frac{(39-25)}{25}+\frac{(21-25)}{25}$

d. $\frac{{(18-25)}^2}{100}+\frac{{(22-25)}^2}{100}+\frac{{(39-25)}^2}{100}+\frac{{(21-25)}^2}{100}$

e. $\frac{{(0.18-0.25)}^2}{0.25}+\frac{{(0.22-0.25)}^2}{0.25}+\frac{{(0.39-0.25)}^2}{0.25}+\frac{{(0.21-0.25)}^2}{0.25}$

Short answer

The correct option is (a).

Step-by-step solution

Given information

Explanation

Null and alternative hypotheses:

$$\begin{gathered} H_0:pR=pT=pP=pH=0.25 \\ {H}_a:Atleastoneofthe{p}_i’sisincorrect. \end{gathered}$$

Using excel,

This calculation is same as option (a) Hence, option (a) is correct.