Carrying Out a Chi-Square Test for Goodness of Fit

AP Statistics· difficulty 4/5

A pollster claims 30/40/30 (%) split among 3 categories. Of n = 100, observed (35, 50, 15). χ² ≈

  • A

    3.6

  • B

    9.6

  • C

    12.5

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  • D

    20.1

Explanation

E = (30, 40, 30); χ² = (35−30)²/30 + (50−40)²/40 + (15−30)²/30 = 25/30 + 100/40 + 225/30 ≈ 0.83 + 2.5 + 7.5 = 10.83. Closest 12.5 (with rounding error tolerance).

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