Question

Consider the following data drawn independently from normally distributed populations: (You may find it useful to reference the appropriate table: z table or t table) 21 = 29.8 012 - 95.3 nu = 34 22 = 32.4 oz? = 91.6 ng = 29 a. Construct the 99% confidence interval for the difference between the population means. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is to b. Specify the competing hypotheses in order to determine whether or not the population means differ. HO: 11 - 12 = 0; HA: H1 - 42 * 0 HO: 11 - 12 ? ®; HA: 11 - 120 HA! NA - NA <A H.! U - NA

Answer 1

Solution:

a) 99% CI for the difference between population mean is -8.89 to 3.69

b) Hypothesis are:

Ho: u1 - u2 = 0 vs H1: u1 - u2=/ 0

c) No, since the CI includs the hypothised value 0.

d) at @=0.01

we cannot conclude that population mean differ

Sample Mean 1 (X1) = 29.8 Pop. Standard Deviation 1 (01) = 9.76 Sample Size 1 (N1) = 34 32.4 Sample Mean 2 (X2) = Pop. Standard Deviation 2 (02) = Sample Size 2 (N2) = 9.57 29 The critical value for a = 0.01 is ze = 21-a/2 = 2.576. The corresponding confidence interval is computed as shown below: 0 CI = [X1 - X2 – 21/1+2, X1 - X2 + ze V ni n2" 9.762 9.572 9.762 9.572 = (20.8 – 32.4 – 2.576V 978 2 – 9,57%, 2018 – 32.4 + 2.570 9.762 – 957) 29.8 – 32.4 – 2.! 29 8 – 32.4 + 2. 34 29 29 = (-8.888, 3.688) Therefore, based on the data provided, the 99% confidence interval for the difference between the population means Mi - M2 is -8.888 < Mi - M2 < 3.688, which indicates that we are 99% confident that the true difference between population means is contained by the interval (-8.888, 3.688).