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Carrying Out a Chi-Square Test for Goodness of Fit

AP Statistics· difficulty 3/5

A teacher believes student birthdays are distributed equally across the four seasons. In a sample of 80 students, observed counts are: Winter 14, Spring 22, Summer 26, Fall 18.

Observed and Expected Counts Winter Spring Summer Fall O=14 O=22 O=26 O=18 E=20 E=20 E=20 E=20

What is the chi-square test statistic?

  • A

    5.6

  • B

    3.2

  • C

    2.4

  • D

    4.0

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Explanation

Chi-square = sum of (O-E)^2/E = 36/20 + 4/20 + 36/20 + 4/20 = 80/20 = 4.0.

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