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:

Which of the following is false?

a. A chi-square distribution with k degrees of freedom is more right-skewed than a chi square distribution with $k+1$ degrees of freedom.

b. A chi-square distribution never takes negative values.

c. The degrees of freedom for a chi-square test are determined by the sample size.

d. $P(\chi 2>10)$ is greater when $df=k+1$ than when $df=k$

e. The area under a chi-square density curve is always equal to $1$

Step by step solution

01

Given information

02

Calculation

Option c is wrong among the possibilities presented. The number of categories determines the degrees of freedom of a chi-square test. $df=c-1$ is the formula. As a result, sample size has no bearing on degrees of freedom.

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