Question

Three different models of automobiles (A, B, and C) were compared for gasoline consumption. For each model of car, fifteen cars were randomly selected and subjected to standard driving procedures. The average miles/gallon obtained for each model of car and sample standard deviations are shown below.

	Car A	Car B	Car C
Average Mile Per Gallon	42	49	44
Sample Standard Deviation	4	5	3

Use the above data and test to see if the mean gasoline consumption for all three models of cars is the same. Let Alpha = 0.05.

Answer 1

S01E- Given cara carr carc Average mile per Gallon | 42 4q Luu Sample standard deviation / u Three different models of automobiles (A, 13 ande) were compared for gasoline consumption Let M., Mr and Ms define as mean gallon consumption of three different automobile A, B and C nes pestively our testing problem is - Ho: M = M2 = M3=M Hi Ho is not true. since, three different automobile are follocas three different normal distribution with mean M,, My and M3 not respectively and another assumption is 61 = 62=6320 le variance are same Hence, test reduces to equality of mean of three different normal variable

Test: Ho :M, 2 M2 = M3 = M. assumptions: in population follows normal distribution ii) Population our homo scordastic method: Their andependent normal population N(Mi, o) Let (se ......Kini) be mandom variable of sample term N (Mi, on sample meen = x1 = this TINNA V 1 ) [since % = 6] » Vni (8) – M;) N (0,r) ni (x: 34 xų , k-3 sample ventionce = 5 m- (60- Hoi ni (7) 12—0 (1371)5* w X'nica : . ost xºn-3 nag ni

from O&@ are we get - under Ho F = Eni (8 - x)/3- INFkrunt È (93-1)s* /n-3 Test statistic F= (m:-) 57/n-3 is [cun-usi't [ua- usit (uu-us}]} 14 [~ + 5 + 3 ] /u2 F. n-3 =45-3 is [(9) +(16) +(10)/2 14 [16+25+9]/uz 15 (26)/2 14(50)/ur 390/2 700/u2 195 16.66 - 11.7006 2. Reject to if & > F2, 42(0.05) (220.05] f-table value of F2 142 (0.03) = 3.22 Here F=11.7ou> Fr. 42 (0.05) = 3.22 Hence Reject the null hypothesis at level 0.05