The following information is based on independent random samples taken from two normally distributed populations having equal variances: Based on the sample information,determine the 95% confidence interval estimate for the difference between the two population means. A)-6.23

Question

The following information is based on independent random samples taken from two normally distributed populations having equal variances: Based on the sample information,determine the 95% confidence interval estimate for the difference between the two population means. A)-6.23 < (µ₁ - µ₂)< 14.23 B)-4.81 < (µ₁ - µ₂)< 16.81 C)-5.17 < (µ₁ - µ₂)< 15.17 D)-3.25 < (µ₁ - µ₂)< 17.25

Quizplus · Accepted Answer

The 95% confidence interval estimate for the difference between the two population means is calculated using the formula: ( X1 - X2 ) ± tα/2,pooled SE where X1 and X2 are the sample means, tα/2,pooled is the critical value from the t-distribution with degrees of freedom equal to the sum of the sample sizes minus 2, and pooled SE is the standard error calculated as: pooled SE = SQRT [ ( s1^2 / n1 ) + ( s2^2 / n2 ) ] Using the information provided in the question, we have: X1 = 128 X2 = 120 n1 = 20 n2 = 25 s1 = 10 s2 = 12 First, we need to calculate the pooled SE: pooled SE = SQRT [ ( 10^2 / 20 ) + ( 12^2 / 25 ) ] pooled SE = 2.288 Next, we need to calculate the critical value from the t-distribution: tα/2,pooled = t0.025,43 = 2.018 Finally, we can calculate the 95% confidence interval estimate for the difference between the two population means: ( X1 - X2 ) ± tα/2,pooled SE ( 128 - 120 ) ± 2.018(2.288) 8 ± 4.62 3.38 < (µ₁ - µ₂) < 12.62 Therefore, the best choice is C, which is -5.17 < (µ₁ - µ₂) < 15.17.

The Following Information Is Based on Independent Random Samples Taken