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? μd= The true mean DIFFERENCE in stopping distance in feet (Wet – Dry Pavement) Wet – Dry 51 73 56 52 39 68 48 Car # Wet Dry 1 201 150 2 220 147 3 192 136 4 182 130 5 173 134 6 202 7 180 128 8 9 206 158 H0: μd = 0 Ha: μd ≠ 0 Matched Pairs t – test SRS – Stated Approximately Normal Distribution – Graph? PWC Since the P-Value = 0 < α = 0.05 REJECT H0 . Evidence exists supporting a difference in stopping distance between the dry and wet pavement

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

Zero in the Interval and Hypothesis Testing Zero NOT in the Interval H0: μd = 0 Ha: μd ≠ 0 μd= True mean difference between 1st Value and 2nd Value. (1st Value – 2nd Value) = 0 The two values are the same. (1st Value – 2nd Value) ≠ 0 The two values can NOT be the same. Zero NOT 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 H0 and support Ha ≠.

WARM UP (again): 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 and at 60 mph you slam on the breaks. Estimate the Mean difference in stopping distance in feet with a 90% Confidence Interval. Wet – Dry 51 73 56 52 39 68 48 Matched Pairs 1-Sample t – Interval Car # Wet Dry 1 201 150 2 220 147 3 192 136 4 182 130 5 173 134 6 202 7 180 128 8 9 206 158 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. SRS – Stated Approximately Normal Distribution – Graph ? PWC

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Matched Pairs vs. Two Sample EXPERIMENT Matched Pairs vs. Two Sample