l Goodness-of-Fit Tests · Test statistic: O-E x 2 E where 0: actual number observed in each class E;= Expected number, T;.n o 2002 The Wadsworth Group
Goodness-of-Fit Tests • Test Statistic: where Oj = Actual number observed in each class Ej = Expected number, pj • n = j E j E j (O – )2 c 2 © 2002 The Wadsworth Group
llGoodness-of-Fit: An Example Problem 13.20: In a study of vehicle ownership it has been found that 13.5% of u. s households do not own a vehicle with 33.7% owning 1 vehicle, 33.5% owning 2 vehicles and 19.3% owning 3 or more vehicles. The data for a random sample of 100 households in a resort community are summarized below. At the 0.05 level of significance, can we reject the possibility that the vehicle-ownership distribution in this community differs from that of the nation as a whole? #Ⅴ ehicles owned井 Households 20 1 35 23 3 or more 22 o 2002 The Wadsworth Group
Goodness-of-Fit: An Example • Problem 13.20: In a study of vehicle ownership, it has been found that 13.5% of U.S. households do not own a vehicle, with 33.7% owning 1 vehicle, 33.5% owning 2 vehicles, and 19.3% owning 3 or more vehicles. The data for a random sample of 100 households in a resort community are summarized below. At the 0.05 level of significance, can we reject the possibility that the vehicle-ownership distribution in this community differs from that of the nation as a whole? # Vehicles Owned # Households 0 20 1 35 2 23 3 or more 22 © 2002 The Wadsworth Group
l Goodness-of-Fit: An Example Vehicles O O -E;2/E 20 13.5 3.1296 3533.7 0.0501 2333.5 3.2910 3 19.3 0.3777 sum=6.8484 I.H0:7=0.135,丌=0.37,n2=0.335,7+=0.193 Vehicle-ownership distribution in this community is the same as it is in the nation as a whole H,: At least one of the proportions does not equal the stated value. Vehicle-ownership distribution in this community is not the same as it is in the nation as a whole 2002 The Wadsworth Group
Goodness-of-Fit: An Example # Vehicles Oj Ej [Oj– Ej ] 2/ Ej 0 20 13.5 3.1296 1 35 33.7 0.0501 2 23 33.5 3.2910 3+ 22 19.3 0.3777 Sum = 6.8484 I. H0 : p0 = 0.135, p1 = 0.337, p2 = 0.335, p3+ = 0.193 Vehicle-ownership distribution in this community is the same as it is in the nation as a whole. H1 : At least one of the proportions does not equal the stated value. Vehicle-ownership distribution in this community is not the same as it is in the nation as a whole. © 2002 The Wadsworth Group