Question

# est the following hypotheses by using the χ 2 goodness of fit test. H 0: p...

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

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