Question

Assighment Chapter 10 Saved Help Save &Exite Check my w Exercise 10-1 Algo 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) o12 -95.4 1 -29 .93.2 2 27 a. Construct the 95% confidence interval for the difference between the population means (Negative values should be indicated by a minus sign. Round all intermediate calculetions to at least 4 decimal places and final answers to 2 decimal places.) Confidence interval is to Prey 10, 8 Next > o search の

Answer 1

As, we know the population standard deviations of both the groups, we will use z statistic to calculate the confidence interval.

Standard error of the mean difference, se = $\sqrt{(\sigma_1^2/n_1)+(\sigma_2^2/n_2) } = \sqrt{(95.4/29)+(93.2/27) } = 2.5964$

z value for 95% confidence interval is 1.96

Mean difference = 24.7 - 29.6 = -4.9

95% confidence interval is,

-4.9 - 1.96 * 2.5964 to  -4.9 + 1.96 * 2.5964

-9.99 to  0.19