A research firm tests the miles-per-gallon characteristics of three brands of gasoline. Because of different gasoline performance characteristics in different brands of automobiles, five brands of automobiles are selected and treated as blocks in the experiment; that is, each brand of automobile is tested with each type of gasoline. The results of the experiment (in miles per gallon) follow.

	Gasoline Brands
		I	II	III
Automobile	A	18	21	20
B	24	26	27
C	30	29	34
D	23	25	24
E	20	23	24

(a) At ? = 0.05, is there a significant difference in the mean miles-per-gallon characteristics of the three brands of gasoline?

State the null and alternative hypotheses:

State your conclusion . Q Do not reject H0. There is not sufcient evidence to conclude that the mean miles-pergallon ratings for the three brands of gasoline are not all equal. 0 Reject H. There is not sufcient evidence to conclude that the mean miles-pergallon ratings for the three brands of gasoline are not all equal. 0 Reject H0. There is sufcient evidence to conclude that the mean milespergallon ratings for the three brands of gasoiine are not all equal. 0 Do not reject HD' There is sufcient evidence to conclude that the mean miles-per-gallon ratings for the three brands of gasoline are not ail equal. Compare your ndings with those obtained in part (a). O The conclusion is the same as the conclusion in part (a). O The conclusion is different from the conclusion in part {a}. What is the advantage of attempting to remove the block effect? 0 We must remove the block effect in order to detect that there is no signicant difference due to the brand of gasoline. 0 We must remove the block effect in order to detect that there is a signicant difference due to the brand of gasoline. Q There is no advantage to removing the block effect because the conclusion is the same in either case. \f0 He: I\"'1 = \"I; = '""111 Ha: Not all the population means are equal. 0 He: l\"'1 = #1: = \"111 Ha: \"I i \"'11 i #111 O HO: At least two of the population means are equal. Ha: At least two of the population means are different. 0 Ho: Not all the population means are equal. Ha: \"I = \"II 2 \"111 0 He: l\"'1 '3 \"11 \"\"111 Ha: \"I = \"II 2 \