Question

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 8 of each​ brand, assigned at random to the left and right rear wheels of 8 taxis. The tires are run until they wear out and the​ distances, in​kilometers, are recorded in the accompanying data set. Find a 95​% confidence interval for μ1−μ2. Assume that the differences of the distances are approximately normally distributed.

Taxi   Brand A   Brand B
1 44,100   46,300
2 38,500   40,300
3 37,900   38,800
4 48,900   47,600
5 39,600   38,900
6 38,300   42,600
7 48,100   49,100
8 31,500   32,200

Let μ1 be the population mean for brand A and let μ2 be the population mean for brand B. The confidence interval is  ___<μ1−μ2<___ ​(Round to one decimal place as​ needed.)

Answer 1

Mean and standard deviation using AVERAGE(), STDEV.S() are:

For Brand A:

Sample mean, x̅1 = 40862.5

Sample standard deviation, s1 = 5826.5249

Sample size, n1 = 8

For Brand B:

Sample mean, x̅2 = 41975

Sample standard deviation, s2 = 5598.4054

Sample size, n2 = 8

95% Confidence interval for the difference :
                                  
At α = 0.05 and df = 8+8-2 = 14, two tailed critical value, t_c = T.INV.2T( 0.05,14 ) = 2.145