If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: AP®︎/College Statistics>Unit 12

Lesson 1: Chi-square test for goodness of fit

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

You might need: Calculator,Chi-squared table

## Problem

Finn read an article claiming that $50\mathrm{%}$ of Americans have brown hair, $20\mathrm{%}$ have black hair, $20\mathrm{%}$ have blonde hair, and $10\mathrm{%}$ 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
Students$17$$14$$14$$5$
He wants to use these results to carry out a ${\chi }^{2}$ 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?