Question: Let X N (X, 2 X), where the variance 2 X > 0 is unknown. Let Y N (Y , 2 Y ), where the

Let X N (X, 2 X), where the variance 2 X > 0 is unknown. Let Y N (Y , 2 Y ), where the variance 2 Y > 0 is unknown. Consider the hypothesis testing that H0 : 2 X 2 Y = 2.1 versus H1 : 2 X 2 Y > 2.1. Given the following information of the independent random samples: n1 = 8, s 2 X = 6.45, n2 = 11, s 2 Y = 5.23, should H0 be rejected with the significance levels = 0.05? Make a decision using confidence interval.

2. Let X ~ N (ux, o'), where the variance of > 0 is unknown. Let Y ~ N (MY, of), where the variance of > 0 is unknown. Consider the hypothesis testing that Ho 2.1 versus H1 : > 2.1. Given the following information of the independent random samples: n1 = 8, SY = 6.45, n2 = 11, sy = 5.23, should Ho be rejected with the significance levels a = 0.05? Make a decision using confidence interval

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