Indep-Ss t WS4- Social Skills - Worksheet new forrmat

WORKSHEET : Independent-Samples t Test – Example 4 (Social Skills) A psychologist wants to examine the influence of having an older sibling on the development of social skills. She recruited a sample of 19 three-year-old children; half had no siblings (NoSib) and half had at least one older sibling (Sib) who was within 5 years of the child’s age. The children’s scores on a social skills inventory are listed in the tables below. Do these data indicate that having an older sibling has a significant effect on the development of social skills? In other words, do the participants with an older sibling have a different level of social skills than participants with no older siblings? Step 1. State your hypotheses. a. Is it a one-tailed or two-tailed test? Two-tailed b. Research hypotheses H A : Children who have an older sibling will differ from those who do not have an older sibling on social skills. H 0 : Children who have an older sibling will not differ from those who do not have an older sibling on social skills. c. Statistical hypotheses H A : µ sib - µ no sib ≠ 0 H 0 : µ sib - µ no sib = 0 Step 2. Set the significance level (  = .05). Determine the critical value of t. t crit = +/- 2.110

Step 3. Compute the appropriate statistical test using the data provided in the two tables below. Note the sum of squares for each group (copied from above): SS 1 = ¿ 17.6 SS 2 = ¿ 20.001 Sib Group (X 1 ) ¯ X X − X ( X − X ) 2 5 7.2 -2.2 4.84 6 -1.2 1.44 7 -0.2 0.04 8 0.8 0.64 10 2.8 7.84 7 -0.2 0.04 8 0.8 0.64 7 6 8 ΣX = 72 SS 1 = ∑ ( X − X ) 2 = ¿ 17.6 n 1 = 10 df 1 = 9 X = ¿ 7.2 NoSib Group (X 2 ) ¯ X X − X ( X − X ) 2 3 6 4 -0.444 0.197 5 0.556 0.309 4 -0.444 0.197 3 -1.444 2.085 3 -1.444 2.085 7 2.556 6.533 5 0.556 0.309 ΣX 2 = 39 SS 2 = ∑ ( X − X ) 2 = ¿ 20.001 n 2 = 9 df 2 = 8 X = ¿ 4.333