Question

Test the following hypotheses by using the x goodness of fit test. HO: pA = 0.40, pB = 0.40, and pc = 0.20 Ha: The population proportions are not PA 0.40, PB 0.40, and Pc-0.20 A sample of size 200 yielded 40 in category A 140 in category B, and 20 in category C. Use a 1 and test to see whether the proportions are as stated n·。 (a) Use the p-value approach. Find the value of the test statistic. Find the p-value. (Round your answer to four decimal places.) p-value- State your conclusion O Do not reject Ho, we cannot conclude that the proportions differ from 0.40, 0.40, and 02 O Reject Ho. We conclude that the proportions are equal to 0.40, 0.40, and 0.20 Do not reject Ho. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20 O Reject Ho- We conclude that the proportions differ from 0.40, 0.40, and 0.20 (b) Repeat the test using the critical value approach. Find the value of the test statistic. State the critical values for the rejection rule. (If the test is one-tailed, enter NONE for the unused tail. Round your answers to three decimal places.) test statistic s test statistic 2 State your conclusion. O Reject Ho. We conclude that the proportions differ from 0.40, 0.40, and 0.20 O Reject Ho- We conclude that the proportions are equal to 0.40, 0.40, and 0.20 Do not reject Ho. We cannot conclude that the proportions differ from 0.40, 0.40, and 0.20 Do not reject Ho. We cannot conclude that the proportions are equal to 0.40, 0.40, and 0.20

Answer 1

a)

applying chi square goodness of fit test:

	relative	observed	Expected	residual	Chi square
category	frequency	Oi	Ei=total*p	R2i=(Oi-Ei)/√Ei	R2i=(Oi-Ei)2/Ei
A	0.400	40	80.00	-4.47	20.000
B	0.400	140	80.00	6.71	45.000
C	0.200	20	40.00	-3.16	10.000
total	1.000	200	200		75.000

test statistic =75.00

p value =0.0000

reject Ho we conclude that the proportions differ from 0.4 ; 0.4 and 0.2

b)

test statistic =75.000

critical value test statsitic <= None

test statsitic >=9.210
conclusion:

reject Ho we conclude that the proportions differ from 0.4 ; 0.4 and 0.2