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 P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?

a. Because $0.0129$ is less than $\alpha =0.05$ reject $H_0$ . There is convincing evidence that the food choices are equally popular.

b. Because $0.0129$ is less than $\alpha =0.05$ reject $H_0$ There is not convincing

evidence that the food choices are equally popular.

c. Because $0.0129$ is less than $\alpha =0.05$ reject $H_0$ . There is convincing evidence that the food choices are not equally popular.

d. Because $0.0129$ is less than $\alpha =0.05$ fail to reject $H_0$ There is not convincing evidence that the food choices are equally popular.

e. Because $0.0129$ is less than $\alpha =0.05$ fail to reject $H_0$ There is convincing

evidence that the food choices are equally popular.

Short answer

The correct option is (b).

Step-by-step solution

Given information

Explanation

Null and alternative hypotheses:

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

The $p-$value $=0.0129$

Level of significance $=a=0.05$

A claim should be the basis for the decision.

Decision: Because the 0.0129 is less than a = 0.05 reject H0. There isn't enough information to suggest that the meal options are equally popular. Hence, option b is correct