Free Printable Chi Square and Goodness of Fit

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Chi Square and Goodness of Fit

Total questions: 15

Worksheet time: 32mins

Name

Class

Date

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.

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?

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

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

Impossible to tell from the information given

10.

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?

11.

Marshall wants to test the hypothesis that the grade obtained in Math is independent of the grade obtained in English. He carries out the $\chi^2$ test at 5% significance level and determines that the $\chi^2$ test statistic is 9.46 and the p-value if 0.0238. The critical value is found 7.82. What conclusion should he draw and why?

Grade in Math is independent of grade in English because the $\chi^2$ test statistic is greater than the critical value.

Grade in Math is independent of grade in English because the p-value is less than the significance level.

Grade in Math is not independent of grade in English because the $\chi^2$ test statistic is greater than the critical value.

12.

For any hypothesis test, which of the following conditions would lead you to reject the null hypothesis and accept the alternative?

The calculated p-value is less than the significance level of the test

The calculated p-value is less than the critical value

The calculated test statistic is less than the significance level of the test

The calculated test statistic is less than the critical value

13.

In both chi square tests, observed frequencies and expected frequencies are used to calculate the p-value

True

False

14.

The chi squared test is used to compare the means between two or more populations.

True

False

15.

Use a goodness of fit test to determine if high school principals believe that students are absent equally during the week or not.

True

False

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Chi Square and Goodness of Fit

Total questions: 15

Worksheet time: 32mins

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