Adm2304 Assignment 2
Question 1: Available on MyStatLab.
Question 2:
Two polls (each based on a random sample of 1000) released just before the recent Ontario provincial election seemed to suggest conflicting outcomes.
The breakdown in percentages for the two polls were:
Liberal PC NDP Green
Angus Reid 33% 36% 26% 5%
Ekos 37.7% 31.5% 23.3% 5.9%
(a) Test at the .05 level of significance whether the data constitute evidence of a real overall disagreement between the two polls.
(b) In particular, test whether the data constitute evidence of a real disagreement between the levels of support for the PC party between the two polls. Use the
.05 level of significance. AnswerOij | Liberal | PC | NDP | Green | Row Totals | Angus Reid | 330 | 360 | 260 | 50 | 1000 | Ekos | 377 | 315 | 233 | 59 | 984 | Column Totals | 707 | 675 | 493 | 109 | 1984 |
a) Test of homogeneity
H0: No real overall disagreement between the two polls
HA: H0 is not true. There is a real overall disagreement between two polls
α = 0.05 df = (r-1)*(c-1) = (2-1)(4-1) = 1*3 = 3
For df = 3; chi-square, based on 0.05 level = 7.8417
Expected observation = Row Total*Column Total/Grand Total
Eij | Liberal | PC | NDP | Green | Row Totals | Angus Reid | 356.3508 | 340.2218 | 248.4879 | 54.93952 | 1000 | Ekos | 350.6492 | 334.7782 | 244.5121 | 54.06048 | 984 | Column Totals | 707 | 675 | 493 | 109 | 1984 |
(Oij – Eij) | Liberal | PC | NDP | Green | Row Totals | Angus Reid | -26.3508 | 19.77823 | 11.5121 | -4.93952 | 0 | Ekos | 26.35081 | -19.7782 | -11.5121 | 4.939516 | 0 | Column Totals | 0 | 0 | 0 | 0 | 0 |
Chi-Square Test: Liberal, PC, NDP, Green
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Liberal PC NDP Green Total 1 330 360 260 50 1000 356.35 340.22 248.49 54.94 1.949 1.150 0.533 0.444
Question 2:
Two polls (each based on a random sample of 1000) released just before the recent Ontario provincial election seemed to suggest conflicting outcomes.
The breakdown in percentages for the two polls were:
Liberal PC NDP Green
Angus Reid 33% 36% 26% 5%
Ekos 37.7% 31.5% 23.3% 5.9%
(a) Test at the .05 level of significance whether the data constitute evidence of a real overall disagreement between the two polls.
(b) In particular, test whether the data constitute evidence of a real disagreement between the levels of support for the PC party between the two polls. Use the
.05 level of significance. AnswerOij | Liberal | PC | NDP | Green | Row Totals | Angus Reid | 330 | 360 | 260 | 50 | 1000 | Ekos | 377 | 315 | 233 | 59 | 984 | Column Totals | 707 | 675 | 493 | 109 | 1984 |
a) Test of homogeneity
H0: No real overall disagreement between the two polls
HA: H0 is not true. There is a real overall disagreement between two polls
α = 0.05 df = (r-1)*(c-1) = (2-1)(4-1) = 1*3 = 3
For df = 3; chi-square, based on 0.05 level = 7.8417
Expected observation = Row Total*Column Total/Grand Total
Eij | Liberal | PC | NDP | Green | Row Totals | Angus Reid | 356.3508 | 340.2218 | 248.4879 | 54.93952 | 1000 | Ekos | 350.6492 | 334.7782 | 244.5121 | 54.06048 | 984 | Column Totals | 707 | 675 | 493 | 109 | 1984 |
(Oij – Eij) | Liberal | PC | NDP | Green | Row Totals | Angus Reid | -26.3508 | 19.77823 | 11.5121 | -4.93952 | 0 | Ekos | 26.35081 | -19.7782 | -11.5121 | 4.939516 | 0 | Column Totals | 0 | 0 | 0 | 0 | 0 |
Chi-Square Test: Liberal, PC, NDP, Green
Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts
Liberal PC NDP Green Total 1 330 360 260 50 1000 356.35 340.22 248.49 54.94 1.949 1.150 0.533 0.444