Question

Two samples are taken with the following sample means, sizes, and standard deviations īj = 29 12 = 36 71 = 72 n2 = 53 81 = 482 = 3 We want to estimate the difference in population means using a 86% confidence level. What distribution does this require? Oz Ot, df = 123 NOTE: The more accurate df formula, used above, is: 2 + 1 72 df 2 2 + - ni 12 1 12 What is a? What is the critical value for the confidence interval? NOTE: Use the df given in the question above, 123 Use Technology The 86% confidence interval is: –7.93 < 1 - 12 < - 6.07 Does this interval include 0? What does that decision mean? It excludes 0. The two population means are different It does include 0. The two population means seem to be equal.
help

Answer 1

Correct answer: Option (B) t, df = 123

alpha = 0.14

Critical value = 1.485

Correct answer: option (A) It excludes 0, The two population means are different

since

We need to construct the 86% confidence interval for the difference between the population means H1 - H2, for the case that the population standard deviations are not known. The following information has been provided about each of the samples: Sample Mean 1 (X) = 29 Sample Standard Deviation 1 (si) = 4 Sample Size 1 (N1) = 72 Sample Mean 2 (X2) = 36 Sample Standard Deviation 2 (S2) 3 Sample Size 2 (N2) = 53 Based on the informationa provided, we assume that the population variances are unequal, so then the number of degrees of freedom is computed as follows: (si/nı + s/n,) df 2 = 124.967 + 11+1 12-1

The critical value for a = 0.14 and df = 124.967 degrees of freedom is te = t1-a/2:1–1 = 1.485. The corresponding confidence interval is computed as shown below: Since we assume that the population variances are unequal, the standard error is computed as follows: si si se ni n2 = 42 V 72 + 32 53 0.626 Now, we finally compute the confidence interval: CI (X1 - X2 - te x se, X1 - X2 + te x se) (29 – 36 – 1.485 x 0.626, 29 – 36 +1.485 x 0.626) (-7.93, -6.07) Therefore, based on the data provided, the 86% confidence interval for the difference between the population means ji – p2 is -7.93 <li - H2 <-6.07, which indicates that we are 86% confident that the true difference between population means is contained by the interval (-7.93, -6.07).