9.4 Notes Testing Involving Paired Differences (Dependent Samples)

Procedure for Hypothesis Testing Paired Differences 1)Null Hypothesis – 2)Alternate Hypothesis - 3)Use α and t-table to determine the critical value(s) (t c ) for the critical region(s) Degrees of Freedom (d.f.) = 4)Enter the differences of paired data into a List. You can put each list in separately and then command another list to subtract the two. This is especially helpful on decimals. 5)Using T-Test in calc., calculate the statistical value (t) using List from step 4. 6)State conclusion

Ex. 1 A team of heart surgeons at Saint Ann’s hospital knows that many patients who undergo corrective heart surgery have a dangerous buildup of anxiety before their scheduled operations. The staff psychiatrist at the hospital has started a new counseling program intended to reduce their anxiety. A test of anxiety is given to patients who know they must undergo heart surgery. Then each patient participates in a series of counseling sessions with the staff psychiatrist. At the end of the counseling sessions, each patient is retested to determine anxiety level. In the table below, higher scores mean higher levels of anxiety. From the data can we conclude that counseling is beneficial? Test at α = 1% Anxiety Scores PatientBefore CounselingAfter Counseling Jan12176 Tom9393 Diane10564 Barbara Mike13082 Bill9880 Frank14279 Carol11867 Alice12589

Ex. 2 Do educational toys make a difference in age at which a child learns to read? To study this question, six pairs of identical twins of preschool age were randomly selected. From each pair, one member was randomly selected to spend 2 hours each day for 6 months in a room well supplied with “educational” toys. The other twin spent 2 hours in a room with non-educational toys. For each twin the data item recorded is the age in months when the child began reading at the primary level. Test to see if the use of educational toys make a difference in the age at which a child learns to read? Use α = 1% Reading ages for Identical Twins (in months) Twin PairsUsed Educational ToysDid Not Use Ed. ToysReading Age (months)

Assignment Day 1 P. 449 #3, 4, 5, 8, 11, 18 Assignment Day 2 P. 450 #10, 12, 16, 17, 19