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 |
H_{a}: |
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 H_{0}. 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) | O_{i} | E_{i}=total*p | R^{2}_{i}=(O_{i}-E_{i})/√E_{i} | R^{2}_{i}=(O_{i}-E_{i})^{2}/E_{i} |
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 X^{2} = | 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
Get Answers For Free
Most questions answered within 1 hours.