Question

est the following hypotheses by using the χ ² goodness of fit test.

H 0:	p A = 0.4, p B = 0.2, and p C = 0.4
Ha:	The population proportions are not p A = 0.4 , p B = 0.2 , and p C = 0.4

A sample of size 200 yielded 50 in category A, 120 in category B, and 30 in category C. Use  = .01 and test to see whether the proportions are as stated in H₀. Use Table 12.4.

a. Use the p-value approach.

χ ² =   (to 2 decimals)

The p-value is Selectless than .005between .005 and .01between .01 and .025between .025 and .05between .05 and .10greater than .10Item 2

Conclusion:
SelectConclude the proportions differ from 0.4, 0.2, and 0.4.Cannot conclude that the proportions differ from 0.4, 0.2, and 0.4.Item 3

b. Repeat the test using the critical value approach.

χ ² _.01 =   (to 3 decimals)

Conclusion:
SelectConclude the proportions differ from 0.4, 0.2, and 0.4.Cannot conclude that the proportions differ from 0.4, 0.2, and 0.4.Item 5

Answer 1

a)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency(p)	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.4000	50	80.0000	-3.35	11.250
B	0.2000	120	40.0000	12.65	160.000
C	0.4000	30	80.0000	-5.59	31.250
total	1.000	200	200		202.5000
test statistic X2 =		202.50

The p-value is  less than .005

Conclude the proportions differ from 0.4, 0.2, and 0.4

b)

Crtiical value χ ²_.01 =9.210

Conclude the proportions differ from 0.4, 0.2, and 0.4