Chi Square Lesson

What is the purpose of a Chi-Square test?

• To determine if there is a significant difference between the observed and expected values in an experiment.

• To determine if there is a statistically significant difference between the observed and expected values in an experiment.

• To do extra math.

• To conclusively prove that your null hypothesis is true or false.

Which significance level (p value) do you look at when finding the critical value?

• .50

• .10

• .05

• .01

How do you find critical value?

• where degrees of freedom lines up with significance level (p-value)

• where significance level (p-value) lines up with chi-square

• the difference between total and chi-square

• degrees of freedom minus significance level (p-value)

How do you find degrees of freedom?

• the number of categories + 1

• the number of categories - one

• total number of categories divided 2

• total number of experiments times 2

Observed in the wild are 10 circles, 20 squares and 30 triangles. The ratio for this particular population is 2:3:5

observed: 10 circles expected: 12

observed 20 squares expected : 18

observed 30 triangles expected: 30

How many degrees of freedom are there in this experiment?

• 1

• 2

• 3

• 4

Tags

NGSS.HS-LS3-3

What are the degrees of freedom for the following χ² test?

• 6
• 2
• 5
• 36

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. 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?" Here are the data in the table provided. The Chi-square value is 11. Which of the following is the most appropriate conclusion?

• The chi-square value is less than the critical value and the null hypothesis should be rejected. Students prefer some foods over others.

• The chi-square value is greater than the critical value and the null hypothesis should be rejected. Students prefer some foods over others.

• Students do not prefer one food type over another as proven by the chi-square test.

• The data is inconclusive.

Recent revenue shortfalls in a mid-western state led to a reduction in the state budget for higher education. To offset the reduction, the largest state university proposed a 25% tuition increase. It was determined that such an increase was needed simply to compensate for the lost support from the state. Separate random samples of 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors from the university were asked whether they were strongly opposed to the increase, given that it was the minimum increase necessary to maintain the university's budget at current levels. The results are in the table provided. Which null hypotheses would be appropriate for performing a chi-square test to determine if students of a particular class are more opposed to the changes compared to other classes?

• The null hypothesis is that the closer students get to graduation, the less likely they are to be opposed to tuition increases. The alternative is that how close students are to graduation makes no difference in their opinion.

• The null hypothesis is that the mean number of students who are strongly are opposed is the same for each of the 4 years. The alternative is that the mean is different for at least 2 of the 4 years.

• The null hypothesis is that the distribution of student opinion about the proposed tuition increase is the same for each of the 4 years at the university. The alternative is that the distribution is different for at least 2 of the 4 years.

• The null hypothesis is that year in school and student opinion about the tuition increase in the sample are independent. The alternative is that these variables are dependent.

Find the degrees of freedom.

• 4
• 5
• 6
• 7

A chi-square test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely).  The spinner is spun 100 times, and the results are recorded.  The degrees of freedom for the test will be

• 8
• 9
• 10
• 99