onstructing Confidence Intervals If we want to determine the difference between two population means, often the best we can do is construct a confidence interval for the difference. To do so, all we need is a difference between two corresponding sample means and the estimated standard error. The margin of error of a confidence interval for the difference between two population means is equal to a T-distribution critical value multiplied by the estimated standard error. With sample standard deviations used in place of population standard deviations, we use T critical values. E=Tcs21n1+s22n2 With the margin of error computed, the difference between the sample means, x1x2 , is the point estimate for the difference between population means. The corresponding confidence interval is: (x1x2)E . Using interval notation, this confidence interval can be expressed as (x1x2E,x1x2+E) . Let's refer back to the statistics in the previous problem on sleep duration for the two groups of children. Recall that the first group of children all watched their screens for less than three hours on the given day. The second group of children all watched their screens for more than three hours that day. Less than 3 hours More than 3 hours Sample Mean: x 7.44 hours 6.78 hours Sample Standard Deviation: s 1.05 hours 0.63 hours Sample Size: n 18 14