Question

solve it on paper

62.6 used on Problem 9.43, 9.78 & 9.44; page 295) A taxi company is trying to decide whether to purchase brand-1 or brand-2 tires for its fleet of taxis. To estimate the difference in the two brands, an experiment is conducted using 12 of each brand. The tires are run until they wear out. The results are: Brand 1: ni = 12, X = 36,700 kilometers, s} = 5,200 kilometers. Brand 2: n2 = 12, = 38,100 kilometers, s} = 6,000 kilometers. a. Compute a 95% confidence interval for H1 - U2 assuming the populations to be approximately normally distributed. You may NOT assume that the variances are equal. Comment. b. Construct a 90% confidence interval for 07/oz. Were we justified in assuming that for oị * oz when we constructed the confidence interval for H1 - H22 Comment.

Answer 1

a) Given X = 36, to cm , I2 = 38,100 km S;' = 5,200 km , S," = 6,000 km no = m = 12 S, = 15200 - 42.1110, S = (6000 = 77.4597 954. ( ; - 1-C (-0.950.or de (silni + slm) - 2 =23868 (Slo) (+) mit B tertical = 2.0651 C1 = (1-1) 1 tala u 77 4597 7- (1 12 (36 700 - 38100) + 2.065 x = (-1463-077, - 1336-928) 95% confident that fue difference befeeren ppulation means is certained by interval y confidence internal for orlor = 5 10. Mes el terms] , and we are 11 and 1 Enh). ICE 1-090 =0 / Foilice - 2.82 90%. C1: 5200/2.80) Tooo ) 5200I 2000 (2.87 2.444 0-3073 !, : 0, from the interval we have

c)

	34500	36700
	45500	46800
	36700	37600
	32000	31200
	48400	47800
	32800	36300
	38100	38800
	30200	31500
Mean	37275	38337.5
SD	6525.062	6169.496
n	8	8

= 37245, 12 = 38 337.5 S = 6525.062, Su = 6169.4976 nas, n=8 of = (silnit 8/m) - 2 = 15.944. (s (mi) 17,9% nitl mtl (I) part A 1 -(: -0.99: 0.01 te = 2.922 ( use t table) - (29285 - $1237-) + 2-12 x 625 cos a cream men = -1062.5+ (2.922 x 3174.854) = (-10339.866,8294.966) 99% confident that the true difference between pop meaty is contained by the interval.

Note : For critical values use t table