A confidence interval may be constructed for the difference between population means. The confidence interval is a range of values that, in the long run, includes the unknown difference between population means a certain percent of the time. If both positive and negative values appear in a confidence interval, no single interpretation is possible. The inclusion of a zero value in the range indicates that the variable being studied may have (17) The t test for two independent samples assumes that both underlying populations are (18) and have (19) variances. If sample sizes are (20) and violations of these assumptions will be of little concern. The pooled variance estimate can be obtained by combining the variance common to both populations. The pooled variance estimate is the most accurate estimate of the variance (assumed to be the same for both populations) based on a combination of the two sample variances. The degrees of freedom for the pooled variance estimate equal the sum of the two sample sizes minus two. Two degrees of freedom are lost because the (21) in each of the two samples are expressed as (22) Frnrn tl'mir rnqnnr'vn qnmnln manna