Question

Test the following hypotheses by using the χ2 goodness of fit test.

H0: pA = 0.2, pB = 0.4, and pC = 0.4

Ha: The population proportions are not pA = 0.2, pB = 0.4, and pC = 0.4

A sample of size 200 yielded 40 in category A, 120 in category B, and 40 in category C. Use = .01 and test to see whether the proportions are as stated in H0.

A) Use the p-value approach.

X^2_____

a.) Repeat the test using the critical value approach.

χ²_.01= ______ (to 3 decimals)

χ2 =_________ (to 2 decimals)

Answer 1

here applying chi square test;

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.2	40	40.00	0.00	0.000
B	0.4	120	80.00	4.47	20.000
C	0.4	40	80.00	-4.47	20.000
total	1.000	200	200		40.000

A)   Use the p-value approach

X² =40.000

p value =0.0000

a)

Repeat the test using the critical value approach.

X²_0.01 =9.210

X² =40.00