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 Design AND Conduct a Two-sample t-Test (both samples n =6) experiment to determine if age significantly decreased Design AND Conduct a Matched Pairs t-Test (n = 6) experiment to determine if age significantly decreased.

Two-Sample vs. Matched Pairs Randomly Choose 2 samples of 6 counties, 6 B & 6 A. County #Before 04After 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 = _______

Two-Sample vs. Matched Pairs Randomly Choose 6 counties. County #Before 04After 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 = _______

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.

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.

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 Wet – Dry Dry 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

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 ft and ft. 1.SRS – Stated 2.Approximately Normal Distribution – Graph Car # WetDry Wet – Dry Dry Matched Pairs 1-Sample t – Interval

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 Wet – Dry Dry 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

EXPERIMENT Matched Pairs vs. Two Sample