## Related questions with answers

Select the best answer. The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the following 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: Asian food, Mexican food, pizza, or hamburgers?" 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 Asian food. (c)

$H_0: n_A = n_M = n_P = n_H = 25,$

where

$n_A$

is the number of students in the school who would choose Asian food, and so on. (d)

$H_0: p_A = p_M = p_P = p_H = 0.25,$

where

$p_A$

is the proportion of students in the school who would choose Asian food, and so on. (e)

$H_0: \hat{p}_A = \hat{p}_M = \hat{p}_P = \hat{p}_H = 0.25,$

where

$\hat{p}_A$

is the proportion of students in the sample who chose Asian food, and so on.

Solution

VerifiedWe expect that each type of food is equally popular.

Since there are 4 types of food, we would then expect a proportion of 1 out of 4 for each type of food.

$p=\dfrac{1}{4}=0.25$

The null hypothesis states that the specified distribution of the categorical variable is correct. Moreover, the statement needs to be about the proportions in the population:

$\begin{matrix}H_0:p_R=p_T=P_p=P_h=0.25\text{, where }p_R\text{ is the proportion of students}\\ \text{ in the school who would chose ramen, and so on}\end{matrix}$

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