Chapter 11: Q 19. (page 718)

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. $H_{0} : μ = 25$ where $μ =$ 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. $H_{0} : n R = n T = n P = n H = 25$ where $n R$ is the number of students in the school who would choose ramen, and so on.
d. $H_{0} : p R = p T = p P = p H = 0.25$ where $p R$ 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.

Expert verified

The correct option is (d).

Step by step solution

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

Total count $= 100$

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

Therefore, $p r o p o r t i o n = \frac{1}{4} = 0.25$

Null and alternative hypotheses:

$H_{0} : p R = p T = p P = p H = 0.25 H_{a} : A t l e a s t o n e o f t h e p_{i} ’ s i s i n c o r r e c t .$

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