Run a goodness-of-fit test with the chi square formula. Enter observed counts and hypothesized proportions or a genetics cross ratio to get expected counts, the per-cell contribution heatmap, the P-value, and the full AP write-up.
The Chi-Square Goodness-of-Fit Procedure Builder walks through the whole AP Statistics procedure. Enter observed counts with equal proportions, your own hypothesized proportions, or a genetics cross ratio such as 9:3:3:1, and see the expected counts, every (O − E)²/E contribution, and the shaded rejection region.
It applies the chi square formula χ² = Σ (O − E)² / E with df = k − 1, checks the Large Counts condition, reports the tabled critical value, and assembles the State / Plan / Do / Conclude write-up in the context of your problem.
The chi square formula is χ² = Σ (O − E)² / E, where O is each observed count and E is the expected count under the null hypothesis. Degrees of freedom are k − 1, one less than the number of categories.
Multiply the total sample size by each hypothesized proportion: E = n × p. For a genetics cross, convert the ratio to proportions first — a 9:3:3:1 dihybrid cross becomes 0.5625, 0.1875, 0.1875, and 0.0625.
Every expected count must be at least 5 for the chi-square approximation to be trustworthy. If a category falls short, the test is still computed, but you should report the condition as not met when interpreting the P-value.
Compare the P-value to α. If the P-value is less than α, reject H₀ and say you have convincing evidence that the true proportions differ from the hypothesized values; otherwise fail to reject H₀ — always stated in the context of the study.
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