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AP®︎/College Statistics

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

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?

AP®︎/College Statistics

Course: AP®︎/College Statistics > Unit 12

Problem