Topics: Null hypothesis, Statistical hypothesis testing, Non-parametric statistics Pages: 4 (747 words) Published: November 15, 2011
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:
LiberalPC 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

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