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In: Statistics and Probability

Independent random sampling from two normally distributed populations gives the results below. Construct a 95 %...

Independent random sampling from two normally distributed populations gives the results below. Construct a 95 % confidence interval estimate of the difference between the means of the two populations. η1 ¬= 82 (X_1 ) ̅ = 115 σ1 = 20 η2 = 83 (X_2 ) ̅ = 100 σ2 = 15

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Expert Solution

95% confidence interval for 1 - 2 is

(1 - 2) - Z * sqrt [ 1 / n2 + 2 / n2 ] < 1 - 2 < (1 - 2) + Z * sqrt [ 1 / n2 + 2 / n2 ]

(115-100) - 1.96 * sqrt [ 202 / 82 + 152 / 83) < 1 - 2 < (115-100) + 1.96 * sqrt [ 202 / 82 + 152 / 83)

9.601 <  1 - 2 < 20.399

95% CI is ( 9.601 , 20.399 )

orchestra answered 2 years ago
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