AP®StatisticsCollege BoardExam QuestionsUnits 6-9: InferenceGoodness of Fit (Chi-Square)

Goodness of Fit (Chi-Square) (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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A school principal wants to compare the number of students they have taking each of the eight different AP® classes that they offer with the proportions of students taking the same courses across the state. Which of the following tests could be used to determine whether the proportions of the students taking the different AP® classes for the school differ from state proportions?

  • A chi-square test for independence.

  • A chi-square goodness of fit test.

  • A chi-square test for homogeneity.

  • A matched pairs t-test.

  • A t-test for the slope of a regression line.

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2
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Shayne wants to test the hypothesis that the number of people with a birthday in each month is evenly distributed across the year. He records the birthday month of a sample of people to test this hypothesis. What is the smallest number that his sample size could be?

  • 12

  • 24

  • 60

  • 80

  • 120

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3
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The distribution of different types of fish in a particular lake is described in the following table.

Type of fish

Bass

Trout

Perch

Other

Proportion of fish

35%

24%

18%

23%

Donny wants to know if the distribution of fish in an adjacent lake, where the population of fish is known to be 2,500, follows the same distribution of types of fish. He plans to carry out a chi-square goodness of fit test. Which of the following is a condition for carrying out this test?

  • He samples at least four fish.

  • He samples at least 20 fish.

  • He samples at least 25 fish.

  • He samples at least 28 fish.

  • He observes each type of fish five times.

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4
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A researcher hypothesizes that in a given population, 90% will have a dominant right hand, 9% will have a dominant left hand, and 1% will be ambidextrous. In a random sample of 520 people, 455 people have a dominant right hand, two people are ambidextrous, and the rest have a dominant left hand. What is the chi squared statistic for the goodness of fit test on these data?

  • Less than one.

  • Greater than or equal to one but less than four.

  • Greater than or equal to four but less than seven.

  • Greater than or equal to seven but less than ten.

  • Greater than or equal to ten.

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5
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The table below shows the data for the distribution of different blood types for a group of 80 people who are affected by a particular disease.

Blood type

0

A

B

AB

Number of people

21

37

18

4

The known proportions of different blood types in the population are shown in the table below.

Blood type

0

A

B

AB

Population proportion

0.39

0.32

0.21

0.08

A chi-square goodness of fit test was conducted to determine whether the data provides convincing evidence that the distribution of the sample is different from the distribution of the population. The test statistic was 9.40 with a p-value of 0.0245. Which of the following statements is true?

  • The chi-square statistic has 80 minus 1 equals 79 degrees of freedom.

  • The proportion of people with blood type AB in the sample is the same as the proportion of blood type AB in the population.

  • At the significance level alpha equals 0.05, the data does not provide convincing evidence that the sample distribution is different from the population distribution.

  • A chi-square goodness of fit test is not valid for the data, as one of the observed frequencies is less than five.

  • At the significance level alpha equals 0.10, the data provides convincing evidence that the sample distribution is different from the population distribution.

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