Question

Suppose an engineer wanted to determine whether the gas mixture used increases gas mileage. He constructed a randomized block design and performed tests to measure the gas mileage. The data were determined to come from normally distributed populations and the variances were determined to be equal. Complete parts (a) through (e) below. Mix 1 Mix 2 Mix 3 Car 1 28.3 28.3 28.7 Car 2 26,9 26.9 26.1 26.4 28.5 27.4 Car 3 26.2 26.8 Car 4 25.9 27.3 Car 5 27.9 29.3 Car 6 25.1 24.9 25,9 (Round to two decimal places as needed.) The P-value is (Round to three decimal places as needed.) Do not reject the null hypothesis. There not sufficient evidence at the 0.05 level of significance to conclude that the mean gas mileage for at least one gas mix is different. (d) If the null hypothesis from part (c) was rejected, use Tukey's test to determine which pairwise means differ using a familywise error rate of a 0.05 The Tukey test indicates that H, <H2 = H3 - (e) Interpret the results of the Tukey test in the context of the problem. Based on the results of part (d), what do you conclude? The mileage is the same for mix 1 and mix 2 and decreases for mix 3

Answer 1

Mix 1	2	3
28.3	28.3	28.7
26.9	26.9	27.4
26.2	26.1	26.8
25.9	26.4	27.3
27.9	28.5	29.3
25.1	24.9	25.9
26.7167	26.8500	27.5667	mean
1.2238	1.3708	1.2453	sd

ANOVA Table... Sum of Squares Source of Variation d.f Variance 0.7634 Between Groups: 2.5079 0.4833 2 1.2539 Within Groups:|24.6378 1.6425 15 Total: 27.1456 17 Post-hoc tests... Tukey HSD Post-hoc Test... Group 1 vs Group 2: Diff=0.1333, 95%CI-1.7887 to 2.0553, p-0.9823 Group 1 vs Group 3: Diff -0.8500, 95%CI -1.0720 to 2.7720, p 0.5003 Group 2 vs Group 3: Diff=0.7167, 95%CI--1.2053 to 2.6387, p-0.6070 O.

TS = 0.76

p-value = 0.483

don't reject the null as p-value > alpha

there is not sufficient evidence tp conclude that at least one gas mix is different

d)

if p-value < alpha then there is significant difference in means

here p-value is greater than 0.05 for all 3 cases

hence

the tukey test indicates

3

e)

it is same for all three mixture