A national opinion poll was conducted to evaluate the voting public's opinion concerning whether new EPA regulations on air pollution were stringent enough to protect the public's health. The poll was also interested in determining if there were regional differences in the public's opinion concerning air pollution. The country was divided into our geographical regions (NE, SE, MW, W)for the poll. A random sample of 100 registered voters was obtained from each of six standard metropolitan statistical areas (SMSA's) located in each of the four regions. The data below are the sample proportions, p^ , of people who thought the EPA standards were not stringent enough for the 24 SMSA's. what is the contrast in the four population means in the questions below?

a. Is the proportion of people who thought the EPA's standards are not stringent enough different for the people living in the East compared to the people living in the West?

b. Is the proportion of people who thought the EPA's standards are not stringent enough different for the people living in the Northeast compared to the people living in the other three regions?

c. Is the proportion of people who thought the EPA's standards are not stringent enough different for the people living in the Northeast compared to the people living in the Southeast?

d. Simultaneously test if the three contrasts are different from 0 using an a =0.05 test.

e. Are the three contrasts mutually orthogonal?

SMSA	NE	SE	MW	W
1	0.84	0.43	0.57	0.1
2	0.81	0.35	0.59	0.12
3	0.78	0.27	0.63	0.13
4	0.85	0.4	0.6	0.15
5	0.85	0.28	0.56	0.11
6	0.83	0.33	0.56	0.11