The sociologist thinks that couples married after age 30 will have greater relationship longevity than couples married before age 30. Identify the null and research hypotheses: H0 : H1 : This is a -tailed test. Step 3: Select the sampling distribution and establish the critical region. The sociologist collects data from one sample of couples married after age 30 and another of couples married before age 30. With small samples, the t distribution is used to establish the critical region because the combined less than 100. Marital Longevity Couples Married after Age 30 Couples Married before Age 30 X1 = 29.3 years X2 = 25.6 years s1 = 9 years s2 = 8 years N1 = 51 N2 = 54 Use the t distribution table that follows to find the critical t-score, the value for a t-score that separates the tail from the main body of the distribution, forming the critical region. To use the table, you will first need to calculate the degrees of freedom (df). The degrees of freedom are . With = 0.01, the critical t-score is . df Proportion in One Tail 0.25 0.10 0.05 0.025 0.01 0.005 Proportion in Two Tails 0.50 0.20 0.10 0.05 0.02 0.01 1 1.000 3.078 6.314 12.706 31.821 63.657 2 0.816 1.886 2.920 4.303 6.965 9.925 3 0.765 1.638 2.353 3.182 4.541 5.841 4 0.741 1.533 2.132 2.776 3.747 4.604 5 0.727 1.476 2.015 2.571 3.365 4.032 6 0.718 1.440 1.943 2.447 3.143 3.707 7 0.711 1.415 1.895 2.365 2.998 3.499 8 0.706 1.397 1.860 2.306 2.896 3.355