Question: A school district in a midsized city currently has a

A school district in a midsized city currently has a single high school for all its students. The number of students attending the high school has become somewhat unmanageable, and, hence, the school board has decided to build a new high school. The school board after considerable deliberation divides the school district into two attendance zones, one for the current high school and one for the new high school. The board guaranteed the public that the mean family ­income was the same for the two zones. However, a group of parents is concerned that the two zones have greatly different family socioeconomic distributions. A random sample of 30 homeowners were ­selected from each zone to be interviewed concerning relevant family traits. Two families in zone II refused to participate in the study, even though the researcher promised to keep interview information confidential. One aspect of the collected data was family income. The incomes, in thousands of dollars, produced the following data.
a. Verify that the two attendance zones have the same mean income.
b. Use these data to test the hypothesis that although the mean family incomes are nearly the same in the two zones, zone I has a much higher level of variability than zone II in terms of family income.
c. Place a 95% confidence interval on the ratio of the two standard deviations.
d. For each zone, use your estimates of the zone standard deviations to determine the range of incomes that would contain 95% of all incomes in each of the zones.
e. Verify that the necessary conditions have been met to apply the procedures you used in parts (a)–(c).

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