Question

The following output summarizes the results for a one-way analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon (mpg) obtained while driving the same route. (You may find it useful to reference the g table.) Hybrid 1: ア1-33, n1-20 Hybrid 2:239, n2 - 15 Hybrid 3:29, n3 18 Source of Variation Between Groups Within Groups Total df 1,181.44 1,439.34 2,620.78 MS 590.72 28.79 p-value 0.0000 20.52 50 a. At the 5% significance level, can we conclude that average mpg differs between the hybrids? Yes since the p-value is less than the significance level. Yes since the p-value is not less than the significance level No .since the p-value is less than the significance level No since the p-value is not less than the significance level

Answer 1

a)

Since p-value is less than 0.05 so we reject the null hypothesis.

First option is correct.

b)

Here we have 3 groups. The degree of freedom is

df= 50

Critical value for , df=50 and k=3 is

= 0,05

3.4443.40 - = 3.42

So Tukey's HSD will be

HSD = 0 MSE 1 ni = 3.42 28.79 2 1 - ni +- 1 nj/

Following table shows the intervals

groups (i-j)	xbari	xbarj	ni	nj	HSD	xbari-xbarj	Lower limit	Upper limit	Significant(Yes/No)
mu1-mu2	33	39	20	15	4.4321	-6	-10.43	-1.57	Yes
mu1-mu3	33	29	20	18	4.2157	4	-0.22	8.22	NO
mu2-mu3	39	29	15	18	4.5364	10	5.46	14.54	Yes