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The 95% confidence interval for this difference is (-17.63, 3.21).įirst we performed an F-test of equal variances. Results: The mean age is 7.209 years lower in those without coronary events than among those who had coronary events. Null Hypothesis: The mean age of people with a coronary event between 19 is the same as the mean age of people without a coronary event between 19:Īlternative Hypothesis: The mean age of people with a coronary event between 19 is not the same as the mean age of people without a coronary event between 19:
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The mean age of the group with coronary events was 49.29 (95% CI = 39.86, 58.71) compared to a mean age of 42.08 (95% CI = 35.57, 48.58) for the group without coronary events. PROC TTEST automatically outputs point and interval estimates of the means and standard deviations for each group and for the difference between groups. This p-value is greater than α=0.05, so we fail to reject H 0: μ 1 = μ 2. The t statistic is -1.45 with 18 degrees of freedom, with p = 0.1633. Step 2: Test the null hypothesis of equal means using the t-test assuming equal variances: Since we do not reject the null hypothesis of equal population variances and the boxplots and ratio of variances seem to indicate similar sample variances, we will assume that the population variances are equal and thus use the pooled standard error. The p-value for the F test using SAS is not significant at α=0.05 (p = 0.9446), so we do not reject H 0: σ 1 2 = σ 2 2 To conduct the formal F test we compare the p-value for the F statistic from SAS to 0.05 (which is two-sided here). Further, the ratio of variances is 1.12 also indicating that the two groups have similar sample variances and thus we might assume that they have equal population variances. The boxplots on the previous page seem to indicate that the variances in the two groups are reasonably similar. Step 1: Check equal variance assumption, : σ 1 2 = σ 2 2 Var age /* variable whose means will be compared */ Var var /* variable whose means will be compared */Ĭlass cor /* defines the grouping variable */ Class group /* defines the grouping variable */