![]() The men have higher mean values on each of the other characteristics considered (indicated by the positive confidence intervals). Men have lower mean total cholesterol levels than women anywhere from 12.24 to 17.16 units lower. Notice that the 95% confidence interval for the difference in mean total cholesterol levels between men and women is -17.16 to -12.24. The fourth column shows the differences between males and females and the 95% confidence intervals for the differences. The second and third columns show the means and standard deviations for men and women respectively. The table below summarizes differences between men and women with respect to the characteristics listed in the first column. Had we designated the groups the other way (i.e., women as group 1 and men as group 2), the confidence interval would have been -2.96 to -0.44, suggesting that women have lower systolic blood pressures (anywhere from 0.44 to 2.96 units lower than men). In this example, we arbitrarily designated the men as group 1 and women as group 2. In this example, we estimate that the difference in mean systolic blood pressures is between 0.44 and 2.96 units with men having the higher values. In contrast, when comparing two independent samples in this fashion the confidence interval provides a range of values for the difference. ![]() Note that when we generate estimates for a population parameter in a single sample (e.g., the mean ) or population proportion ) the resulting confidence interval provides a range of likely values for that parameter. The standard error of the difference is 0.641, and the margin of error is 1.26 units. ![]() Our best estimate of the difference, the point estimate, is 1.7 units. Interpretation: With 95% confidence the difference in mean systolic blood pressures between men and women is between 0.44 and 2.96 units. Therefore, the confidence interval is (0.44, 2.96) Next we substitute the Z score for 95% confidence, Sp=19, the sample means, and the sample sizes into the equation for the confidence interval. Notice that for this example Sp, the pooled estimate of the common standard deviation, is 19, and this falls in between the standard deviations in the comparison groups (i.e., 17.5 and 20.1). The ratio of the sample variances is 17.5 2/20.1 2 = 0.76, which falls between 0.5 and 2, suggesting that the assumption of equality of population variances is reasonable.įirst, we need to compute Sp, the pooled estimate of the common standard deviation. Next, we will check the assumption of equality of population variances.
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