Chi Square and Goodness of Fit

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 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?"  Here are the data in the table provided.  The P-value for a chi-square test for goodness of fit is 0.0129.  Which is the following is the most appropriate conclusion?

• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is not convincing evidence that the food choices are equally popular.
• Because 0.0129 is less than α = 0.05, reject H₀.  There is convincing evidence that the food choices are not equally popular.
• Because 0.0129 is less than α = 0.05, fail to reject H₀.  There is convincing evidence that the food choices are equally popular.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.ID.B.5

Python eggs How is the hatching of water python eggs influenced by the temperature of the snake’s nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs that hatched and didn’t hatch.

If the p-value is .08 and you use .05 as your alpha, what is your conclusion for the goodness of fit test.

• Fail to reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

• Reject: We do not have sufficient evidence that distribution of hatched is different for water temperature options

• Fail to reject: We do have sufficient evidence that distribution of hatched is different for water temperature options

• Reject: We do have sufficient evidence that distribution of hatched is different for water temperature options

Aw, nuts! A company claims that each batch of its deluxe mixed nuts contains 52% cashews, 27% almonds, 13% macadamia nuts, and 8% brazil nuts. To test this claim, a quality-control inspector takes a random sample of 150 nuts from the latest batch. The one-way table below displays the sample data. What is the appropriate null hypothesis for this goodness of fit test.

• p₁=p₂=p₃=p₄

• Mixed nut proportions are proportioned the same as they claim

• At least one of the four types in the population is different than expect

• the observed counts are equally distributed

How do you find degrees of freedom for a chi-square goodness of fit test?

• one less than the sample size

• one less than the population

• total number divided 2

• total number times 2

The table shows the number or babies born on each day of the week. Is there evidence that births are more likely on specific days of the week?

• yes, the p value is greater than .05

• no evidence, the p value is less than .05

• yes, the p value is less than .05

• no evidence, the p value is greater than .05

The bigger the chi square statistic, the ________ the p value.

• bigger
• smaller

How many degrees of freedom will be present?

• 4

• 5

• 6

• 7

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

• 6

• 2

• 5

• 36

A student wants to test the hypothesis that favorite car color is independent of gender. He shows people pictures of the same car in 5 different colors, and records their preference. How many degrees of freedom will there be in his  $\chi^2$  test

• 10

• 4

• 8

• Impossible to tell from the information given

A student wants to test the hypothesis that gender affects the number of hours of sport watched on television. He selects 150 people, equally divided between the genders and categorizes them as watching sport "almost never", "sometimes", "regularly". He has 32 people in his sample who watch sport regularly. What is the expected frequency of females who watch sport regularly?

• 24

• 63

• 54

• 16