# solution

Refer to Example 8.6.

a. Apply the Kruskalâ€“Wallis test to determine if there is a difference in the distributions of opinions across the four geographical regions.

b. Does your conclusion differ from the conclusion reached in Exercise 8.17?

Example 8.6

A political action group conducted a national opinion poll to evaluate the voting publicâ€™s opinion concerning whether the new EPA regulations on air pollution were stringent enough to protect the publicâ€™s health. The group was also interested in determining if there were regional differences in the publicâ€™s opinion concerning air pollution. For this poll, the country was divided into four geographical regions (NE, SE, MW, W). A random sample of 100 registered voters was obtained from each of six standard metropolitan statistical areas (SMSAs) located in each of the four regions. The data in Table 8.21 are the sample proportions, p^ , of people who thought the EPA standards were not stringent enough for the 24 SMSAs.

a. Is there a significant difference in the variability of the four regionâ€™s proportion? Use a Â .05.

b. Transform the data using T Â arcsin Â .

c. Compute the sample means and sample standard deviations for the transformed data. Did the transformation yield a stabilization of the variances?

Exercise 8.17

Refer to Example 8.6.

a. Do the data indicate that the populations are not normally distributed?

b. Do the transformed data appear to have a normal distribution?

c. Does a transformation that produces data having equal variances guarantee that the transformed data will be normally distributed?

Example 8.6

A political action group conducted a national opinion poll to evaluate the voting publicâ€™s opinion concerning whether the new EPA regulations on air pollution were stringent enough to protect the publicâ€™s health. The group was also interested in determining if there were regional differences in the publicâ€™s opinion concerning air pollution. For this poll, the country was divided into four geographical regions (NE, SE, MW, W). A random sample of 100 registered voters was obtained from each of six standard metropolitan statistical areas (SMSAs) located in each of the four regions. The data in Table 8.21 are the sample proportions, p^ , of people who thought the EPA standards were not stringent enough for the 24 SMSAs.

a. Is there a significant difference in the variability of the four regionâ€™s proportion? Use a Â .05.

b. Transform the data using T Â arcsin Â .

c. Compute the sample means and sample standard deviations for the transformed data. Did the transformation yield a stabilization of the variances?

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