1. The independent and normally distributed random variables X and Y have known standard deviations of and , respectively. A sample of 36 observations from the X population yielded , and a sample of 49 observations from the Y population resulted in . Using Equation (11.4), find a 99% confidence interval for the mean difference .

2. The American Automobile Assn. (AAA) compared the mean prices per gallon of gasoline in two different metropolitan areas. The mean price per gallon in area X was (n_{X} = 40) and the mean price per gallon in area Y was (n_{Y} = 35). If prior studies reveal that and , find a 95% confidence interval for the mean difference . What assumptions are being made?

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