Main content

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

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:

Color	Brown	Black	Blonde	Red
Students	17	14	14	5

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?

(Choice A)
$\begin{aligned} &\chi^2=5.76; \\ &0.10 <\text{P-value} < 0.15 \end{aligned}$
(Choice B)
$\begin{aligned} &\chi^2=5.76; \\ &0.20 <\text{P-value} < 0.25 \end{aligned}$
(Choice C)
$\begin{aligned} &\chi^2=6.05; \\ &0.10 <\text{P-value} < 0.15 \end{aligned}$
(Choice D)
$\begin{aligned} &\chi^2=6.05; \\ &0.15 <\text{P-value} < 0.20 \end{aligned}$

Stuck?

Statistics and probability

Course: Statistics and probability > Unit 14

Problem