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## Statistics and probability

### Course: Statistics and probability>Unit 14

Lesson 1: Chi-square goodness-of-fit tests

# Test statistic and P-value in a goodness-of-fit test

AP.STATS: VAR‑8 (EU), VAR‑8.F (LO), VAR‑8.F.1 (EK), VAR‑8.F.2 (EK), VAR‑8.G (LO), VAR‑8.G.1 (EK)
You might need: Calculator,Chi-squared table

## Problem

Finn read an article claiming that 50, percent of Americans have brown hair, 20, percent have black hair, 20, percent have blonde hair, and 10, percent have red hair. He wondered if the hair colors of students at his school followed this distribution, so he took a random sample of 50 students and recorded their hair colors. Here are his results:
ColorBrownBlackBlondeRed
Students1714145
He wants to use these results to carry out a \chi, squared goodness-of-fit test to determine if the distribution of hair colors at his school disagrees with the claimed percentages.
What are the values of the test statistic and P-value for Finn's test?