Question

Independent random sampling from two normally distributed populations gives the results below. Find a 99% confidence interval estimate of the difference between the means of the two populations ni 70 X1-377 ƠI :19 n2-34 x2 334 ơ2-29 The confidence interval is < (m-μ2) (Round to four decimal places as needed)

Answer 1

At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval for $\dpi{100} \mu1 - \mu2$ is

($\dpi{100} \bar x1 - \bar x2$) +/- z_0.005 * $\dpi{100} \sqrt{\sigma1^2/n1 &plus; \sigma2^2/n2}$

= (377 - 334) +/- 2.58 * sqrt((19)^2/70 + (29)^2/34)

= 43 +/- 14.1059

= 28.8941, 57.1059

The confidence interval is 28.8941 < $\dpi{100} \mu1 - \mu2$ < 57.1059