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

You might need: Calculator,Chi-squared table

Finn read an article claiming that

50 %

of Americans have brown hair,

20 %

have black hair,

20 %

have blonde hair, and

10 %

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:

Color	Brown	Black	Blonde	Red
Students	$17$ ‍	$14$ ‍	$14$ ‍	$5$ ‍

He wants to use these results to carry out a

χ^{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?

AP®︎/College Statistics