Question

Homework #7 - Chapter 14815 (20pts for turned in on time) 9. (10pts) in a study of breaking performance, a tire manufacturer measured the stopping distance for one of the tire models (Model A). On a test track, a car will make sudden stop at a speed of 60 miles per hour, and the distance in feet) is measured after the car made a complete stop. There are 8 set of tires being tested, and the data is shown below: 145 152 141 143 131 1 26 140 133 (1) (2pts)What is the population of the study? What is the sample of the study? (2) (3pts)Compute the sample statistic: sample mean X, and sample standard deviation s. X 145 152 141 143 131 126 140 133 X (X-X) 138.9 6. 1 138.9 13.1 138. 92 . 1 138.9 138.9 .7. 9 138.91 -12.9 138.9 1.1 138.9 -5.9 Total (x - 2) 3 7.21 171.61 4.41 16.81 6 2.41 166.41 1.21 34.81 494.88 (3) (5pts)If the population standard deviation of the stopping distance is provided as = 6.7 feet. And suppose we can apply Central Limit Theorem, estimate the population mean with a 94% confidence interval. Don't forget to write conclusion using context words.

Answer 1

(1) Population study : average stopping distance for all tires of model A.

Sample study : average stopping distance of 8 sets of tires.

(2)

- Σx 145+152+141+143+131+126+140 +133 2=138.9 x =- Σ(x – x) 494.88 = 8.4082 S=1/- Η η-1 | 7

(3)

Sample mean = 3 = 138.9 Sample size = n = 8 Population S.D = 0 = 6.7 Standard Error = 0/Vn = 6.7/18 = 2.36881 Confidence Level = 94 Significance Level = a = (100-94)% = 0.06 Critical value = z* = 1.88 [Using Excel =ABS(NORMINV(0.06/2,0,1))] Margin of Error = z*(o/Vn )= 1.88*2.36881 = 4.45336 Lower Limit = 3 - Margin of Error = 138.9 -4.45336 = 134.4466 Upper Limit = x + Margin of Error = 138.9 + 4.45336 = 143.3534 Ans: (134.4466, 143.3534)