Question

Independent random samples were selected from two quantitative populations, with sample sizes, means, and variances given below.

		Population
		1	2
Sample Size		39	44
Sample Mean		9.3	7.3
Sample Variance		8.5	14.82

Construct a 90% confidence interval for the difference in the population means. (Use μ₁ − μ₂. Round your answers to two decimal places.)

__________ to ____________

Construct a 99% confidence interval for the difference in the population means. (Round your answers to two decimal places.)

__________ to _____________

Answer 1

a)

df = (sini + s/n2) + - 2 = 80.988 1+1 12+1 The critical value for a = 0.1 and df = 80.988 degrees of freedom is te = tı-a/2;n–1 = 1.664. 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: 83 se ni n2 2.9162 39 + 3.852 44 = 0.745 Now, we finally compute the confidence interval: CI (X1 - X2 – te x se, X1 – X2 +te x se) (9.3 – 7.3 – 1.664 x 0.745, 9.3 – 7.3+1.664 x 0.745) (0.761, 3.239)

b)

2.638. The The critical value for a = 0.01 and df = 80.988 degrees of freedom is to = t1-a/2;n-1 corresponding confidence interval is computed as shown below: Since we assume that the population variances are unequal, the standard error is computed as follows: sz se ni n2 2.9162 39 + 3.852 44 = 0.745 Now, we finally compute the confidence interval: CI (#1 – X2 - tex se, X1 – X2 + te x se) (9.3 – 7.3 -2.638 x 0.745, 9.3 – 7.3 +2.638 x 0.745) (0.035, 3.965)