4.7.C—Calculate an appropriate confidence interval for the difference between two population means

Calculate an appropriate confidence interval for the difference between two population means.

• A point estimate for the difference between two population means is the difference in sample means, x12−x .
• For the difference between population means when the population standard deviations are unknown, the confidence interval can be constructed as point estimate ±(margin of error). The confidence interval for the difference between population means is ( ss2 2 xx12- ) ±+t* 1 2 nn1 2 , where t∗ are the critical values for the central C% of a t-distribution with appropriate degrees of freedom that can be found using technology. The degrees of freedom fall between n12+-n 2 and the smaller of n1 −1 and n2 −1.