Question

Amy has two ways to travel from her home in Norco to her office in Los Angeles. One is to go via the 10 Freeway, and the other is to go via 60 Freeway. In order to determine which way she should travel on a daily basis, Amy has recorded the travel times for samples of ten trips via the 10 Freeway and ten trips via the 60 Freeway. The following table gives the travel times in minutes) for the twenty trips: Travel times in minutes 10 Freeway 70, 73, 78, 74, 72, 74, 72, 70, 71, 70 60 Freeway 68, 80, 72, 72, 77, 74, 74, 75, 72, 75 Assume that the two populations of travel times are normally distributed and that the population variances are equal. Can we conclude, at the 0.1 level of significance, that the mean travel times of the two routes are different? Perform a two-tailed test. Then fill in the table below Carry your intermediate computations to at least three decimal places and round your answers as specified in the table.

Answer 1

Sal lo free way (x) Go free way (4) (X-M12 (Y-My) 2 68 80 34.81 37.2) 5.76 0 36 31.36 2.56 72 3.61 72 7o 73 78 7u 72 74 72 70 71 70 3.61 9.61 77 74 75 72 2.56 0.16 5.176 1.96 5.76 0.01 1:21 3.61 75 EX=724 Ssy=94.90 = 72.4 ; nana = 10 are EY=739 = 56.40 Mx = mean as x=724 My = mean of y= 739 = 73.9 Null hypothesis M = 42 (Average time for both free way equal ) Alternate hypother's Hi 7 Hz (Average time for boter free way different Here we T-test far too Independent means n, eng <30 Standard deviation (papulation) unknown t = Mx - My Un, -1) sy + hal) sa bo) n, th2-2 where S sh 94.9 10.54 10-1 nalues i.e., Mx, My ,n,, na sr & sy we -1.156 (degree of freedom = n, the 2 122) df=18 far above t seare having af = 18 can be calculated by using t- table ; P-value = 0.2624 .. p-value > x (a= oil) so we canclude that mean travel time are same I No] ni Ssx 36.40 9 6:27 n-1 Ssy n-1 the - Putting all get t = P-value far both free ways