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Two independent random samples have been selected. 100 observations from population 1 and 100 from population...

Two independent random samples have been selected. 100 observations from population 1 and 100 from population 2. Sample means ¯x_1=70 and ¯x_2=50 were obtained. From previous experience with these populations, it is known that the variances are σ_1^2=100 and σ_2^2=64. Construct a 95% confidence interval for (μ_1-μ_2 ).

(A) 20±2.15 (B) 20±2.51 (C) 20±2.35 (D) 20±1.15

Math   Statistics-And-Probability   
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Answer #1

95% confidence interval for 1 - 2 is

(1 - 2 ) Z/2 * sqrt [21 / n1 + 22 / n2 ]

(70 -50) 1.96 * sqrt [ 100 / 100 + 64 / 100 ]

20 2.51

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