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:

An appropriate null hypothesis to test whether the food choices are equally popular is

a. $H_0:\mu =25$where $\mu =$the mean number of students that prefer each type of food.

b. $H_0:p=0.25$where p = the proportion of all students who prefer ramen.

c. $H_0:nR=nT=nP=nH=25$where $nR$is the number of students in the school who would choose ramen, and so on.

d.$H_0:pR=pT=pP=pH=0.25$where $pR$is the proportion of students in the school who would choose ramen, and so on.

e. $H_0:p^R=p^T=p^P=p^H=0.25$, where $p^R$is the proportion of students in the sample who chose ramen, and so on.

Short answer

The correct option is (d).

Step-by-step solution

Given information

Explanation

Claim: Every variety of cuisine will be equally well-liked.

Total count $=100$

Divide $1$by$4$ to divide foods in equal proportions.

Therefore, $proportion=\frac{1}{4}=0.25$

Null and alternative hypotheses:

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