27. A manufacturer of a line of breakfast cereals wants to test market a new cereal...

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27. A manufacturer of a line of breakfast cereals wants to test market a new cereal for children. The advertising department is trying to decide between a cartoon bear or a cartoon lion on the front of the box. In a random sample of 160 girls ages 8-15, 95 girls preferred the box with the cartoon bear. In a random sample of 180 boys ages 8-15, 98 boys preferred the box with the cartoon bear. a. Is this convincing evidence that the true proportion of all girls ages 8-15 that prefer the box with the cartoon bear is different from the true proportion of all boys ages 8 - 15 that prefer the box with the cartoon bear? b. Construct a 95% confidence interval for the true difference in the proportion of boys and girls (8-15) that prefer the box woth the cartoon bear. 27. A manufacturer of a line of breakfast cereals wants to test market a new cereal for children. The advertising department is trying to decide between a cartoon bear or a cartoon lion on the front of the box. In a random sample of 160 girls ages 8-15, 95 girls preferred the box with the cartoon bear. In a random sample of 180 boys ages 8-15, 98 boys preferred the box with the cartoon bear. a. Is this convincing evidence that the true proportion of all girls ages 8-15 that prefer the box with the cartoon bear is different from the true proportion of all boys ages 8 - 15 that prefer the box with the cartoon bear? b. Construct a 95% confidence interval for the true difference in the proportion of boys and girls (8-15) that prefer the box woth the cartoon bear.