Question

Problem # 7 (a) A taxi company is trying to decide: whether to purchase brand A or brand B 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 .4: 1- 36,300 kilometers, 15,000 kilometers Brand B: 2-38, 100 kilometers, s26, 100 kilometers. Compute a 95% confidence interval for A- B assuming the populations to be approximately normally distributed. You may not assume that the variances are equal. (b) Referring to part (a), find a 99% confidence interval for μA-ua if a tire from each company is assigned at random to the rear wheels of 8 taxis and the following distance, in kilometers, recorded: Taxi Brand A Brand B 34.400 45.500 36,700 32,000 48,400 32.800 38.100 30.100 36,700 46,800 37.700 31.100 47.800 36,400 38,900 31,500 4 Assume that the differences of the distances are approximately normally distributed.

Answer 1

a) variance are not equal

t-test for two independe samples,

The standard deviation of thedifference between sample means is approximately:

=sqrt( s₁² / n₁ +s₂² /n₂ )

t_alpha/2,df = t_0.025,21 = 2.08

THedifference between means is 38100-36300=1800

95% confidence interval given by-

(x1 bar - x2 bar)+/- t_alpha/2*sqrt( s₁² / n₁ +s₂² /n₂ )

(36300-38100) + / - 2.08**sqrt (5000²/12+6100²/12)

(-1800+/- 4735.903)

(-6535.903,2935.903)