Question

6. You are interested in buying a car that gives good gas mileage. You have narrowed down the choices to 3 types of car models: C1, C2 and C3. You wish to test the following: Ho: H = H2 = H3 Hy: at least two of the means differ The gas mileage for each model CI, C2 and C3, from a sample of 5 cars for each model is given below. Column 1 represents the index i, for each observation. Columns (2), (3) and (4) are the mileage entries for each of the 5 sample points for each model. Gas Mileage per gallon for 3 models C1, C2 & C3 1 (2) (3) 4) C1 C2 17 24.2 26 2 20.4 22 19.8 3 24 17.8 24.4 15.8 16.2 17.8 21.822.8 C3 1 4 16 5 1 a. What are the dependent and independent variables here? b. How many populations are we talking about here? c. Compute SSI, SS2, SS3 and SSW. What does SSW represent? d Compute the overall mean as X and SSB. What does SSB represent? e Compute MSB and MSW 1. Use the answers above to summarize the table: Source of Variation Between Group Within-Group Total Sum of Squares SSB - SSW- SST - Degrees of freedom Mean Square MSB -- MSW- g. Can we reject the null? Can we close our eyes and buy any model randomly? Show all steps, involved in making this decision.

Answer 1

(a) The dependent variable is gas mileage and the independent variables are the models of car.

(b) The population is all the car models.

(c) SSW means the sum of squares in the within group.

SSW = 149.04

(d) X = 20.04

SSB = 19.6

SSB means the sum of squares between groups.

(e) MSB = 9.8

MSW = 12.42

(f)

Source	SS	df	MS	F	p-value
Treatment	19.600	2	9.8000	0.79	.4765
Error	149.040	12	12.4200
Total	168.640	14

(g) The p-value is 0.4765.

Since the p-value (0.4765) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that there is a difference between means.