Question

Crescent Oil has developed three new blends of gasoline – Blend X, Blend Y and Blend Z, and must decide which blend or blends to produce and distribute. A study of the miles per gallon ratings of the three blends is being conducted to determine if the mean ratings are the same for the three blends.

Five automobiles- 1, 2 3, 4 and 5, have been tested using each of the three gasoline blends and the miles per gallon ratings are shown on the accompanying Excel spreadsheet.

Based on the sample data we would like to determine whether the different blends of gasoline, produce significant differences in the average mpg. We would like to use the methods we have learnt so far in 361A to see if our result is statically significant. (Statistical significance refers to a result that is not likely to occur randomly but rather is likely to be attributable to a specific cause – in this case the different gasoline blends and different cars.)

Automobile	Blend X	Blend Y	Blend Z
1	31	30	30
2	30	29	29
3	29	29	28
4	33	31	29
5	26	25	26

Give

Data description and the business questions to be answered

Answer 1

using excel>data>data analysis>One way ANOVA

we have

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Blend X	5	149	29.8	6.7
Blend Y	5	144	28.8	5.2
Blend Z	5	142	28.4	2.3
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	5.2	2	2.6	0.549296	0.591207	3.885294
Within Groups	56.8	12	4.733333
Total	62	14

the null and alternative hypothesis is

Ho:uX=uY=uZ

Ha :at least one mean Blend is different

we have

From the output F stat is 0.5493 which is less than the F critical 3.8853 so we do not reject Ho and conclude that . the different blends of gasoline, produce significant differences in the average mpg.