Setting Up a Chi-Square Goodness of Fit Test

AP Statistics· difficulty 2/5

A researcher wants to perform a chi-square goodness-of-fit test on a categorical variable with 5 levels using a sample of 50 observations. The expected counts under H0 are 20, 15, 8, 4, 3.

Expected Counts A B C D E 20 15 8 4 3

Which condition is violated?

  • A

    Normality

  • B

    Random sample

  • C

    Large counts (some E < 5)

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  • D

    Independence

Explanation

The large-counts condition requires all expected counts >= 5. Here E = 4 and E = 3 fall below this threshold, so the condition is violated.

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