In: Statistics and Probability
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
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 )