2. 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 = REJECT H0 . Evidence exists supporting a difference in stopping distance between the dry and wet pavement

7. 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)

8. 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 ≠.

9. 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 ft and ft.
SRS – Stated
Approximately Normal Distribution – Graph ? PWC

10. PAGE 587: 7, 8,10, 13

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