2. Two-Sample vs. Matched Pairs The following data indicates the average age of registered voters before and after the 2004 election. Choose 6 counties. County #Before 04After 04 13536 24038 34243 43635 54137 65049 74742 83836 93940 104340 113732 1. 1. Design AND Conduct a Two-sample t-Test (both samples n =6) experiment to determine if age significantly decreased. 2. 2. Design AND Conduct a Matched Pairs t-Test (n = 6) experiment to determine if age significantly decreased.

3. Two-Sample vs. Matched Pairs Randomly Choose 2 samples of 6 counties, 6 B & 6 A. County #Before 04After 04 13536 24038 34243 43635 54137 65049 74742 83836 93940 104340 113732 1. 1. Design AND Conduct a Two- sample t-Test (n =6) experiment to determine if age significantly decreased. μ i = True mean age of voters… i=1 Before 04, i=2 After 04 H 0 : μ 1 = μ 2 H a : μ 1 > μ 2 TWO Sample t – Test 1.SRS – Stated 2. Independent 3. Approximately Normal Distribution – Graph BOTH! t = ________ P-Value = _______ t = ________ P-Value = _______

4. Two-Sample vs. Matched Pairs Randomly Choose 6 counties. County #Before 04After 04 13536 24038 34243 43635 54137 65049 74742 83836 93940 104340 113732 2. 2. Design AND Conduct a Matched Pairs t-Test (n = 6) experiment to determine if age significantly decreased. μ d = True mean difference in age of voters. (Before 04, - After 04) H 0 : μ d = 0 H a : μ d > 0 Matched Pairs t – Test 1.SRS – Stated 2. Not Independent 3. Approximately Normal Distribution Graph differences t = ________ P-Value = _______ t = ________ P-Value = _______

5. Zero in the Interval and Hypothesis Testing Zero in the Interval Confidence Intervals represent the possible differences between the two pair values. If Zero is NOT found in the confidence interval then you have evidence to Reject H 0 and support H a. H 0 : μ d = 0 H a : μ d ≠ 0 μ d = True mean difference between 1 st Value and 2 nd Value. (1 st Value – 2 nd Value) = 0 The two values are the same. (1 st Value – 2 nd Value) ≠ 0 The two values can NOT be the same.

6. Confidence Intervals and Hypothesis Testing Confidence Interval: 1.Confidence Interval: Interpreting Matched-Pairs Intervals We can be C% (95%) Confident that the true mean DIFFERENCE between the two paired values is between (lower bound, upper bound) ● Confidence Intervals and Hypothesis Testing ● Two Sample Inferences vs. Matched Pairs.

7. WARM UP The maker of a new tire claims that his Tires are superior in all road conditions. He claims that with his tires there is no difference in stopping distance between dry or wet pavement. To test this you select an SRS of 9 cars, spike the breaks at 60 mph and recorded skid length in feet. Is there evidence of a difference? μ d = The true mean DIFFERENCE in stopping distance in feet (Wet – Dry Pavement) 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # WetDry 1201150 2220147 3192136 4182130 5173134 6202134 7180128 8192136 9206158 Wet – Dry Dry 51 73 56 52 39 68 52 56 48 Matched Pairs t – test H 0 : μ d = 0 H a : μ d ≠ 0 Since the P-Value = 0 < α = 0.05 REJECT H 0. Evidence exists supporting a difference in stopping distance between the dry and wet pavement

8. Example 1: The maker of a new tire claims that his Tires are superior in all road conditions. An SRS of 9 cars are selected. Estimate the Mean difference in stopping distance in feet with a 90% Confidence Interval. μ d = The true mean DIFFERENCE in stopping distance in feet (Wet – Dry Pavement) We are 90% Confident that the True mean difference in stopping distance in feet between Wet Pavement – Dry Pavement is between 48.671 ft and 61.329 ft. 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # WetDry 1201150 2220147 3192136 4182130 5173134 6202134 7180128 8192136 9206158 Wet – Dry Dry 51 73 56 52 39 68 52 56 48 Matched Pairs 1-Sample t – Interval

9. WARM UP revisted The maker of a new tire claims that his Tires are superior in all road conditions. He claims that with his tires there is no difference in stopping distance between dry or wet pavement. To test this you select an SRS of 9 cars, spike the breaks at 60 mph and recorded skid length in feet. Is there evidence of a difference? μ d = The true mean DIFFERENCE in stopping distance in feet (Wet – Dry Pavement) 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # WetDry 1201150 2220147 3192136 4182130 5173134 6202134 7180128 8192136 9206158 Wet – Dry Dry 51 73 56 52 39 68 52 56 48 Matched Pairs t – test H 0 : μ d = 0 H a : μ d ≠ 0 Since the P-Value = 0 < α = 0.05 there is STRONG evidence to REJECT H 0. There is a difference in stopping distance between the dry and wet pavement

10. EXPERIMENT Matched Pairs vs. Two Sample