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.

QUESTION 2
Petronas has developed two blends of gasoline. Managers are
interested in estimating the difference in mean gasoline mileage
that will be obtained from using the two blends. As part of their
study, they have decided to run a test using the Chevrolet Impala
automobile with automatic transmissions. They selected a random
sample of 100 Impalas using Blend 1 and another 100 Impalas using
Blend 2. Each car was first emptied of all the gasoline in its tank
and...

Do heavier cars really use more gasoline? Suppose a car is
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pounds), and let y be the miles per gallon (mpg).
x
27
43
31
47
23
40
34
52
y
30
20
25
13
29
17
21
14
Complete parts (a) through (d), given Σx = 297, Σy = 169, Σx2 =
11,737, Σy2 = 3861, Σxy = 5845, and r ≈ −0.944.
(a) Verify...

Do heavier cars really use more gasoline? Suppose a car is
chosen at random. Let x be the weight of the car (in hundreds of
pounds), and let y be the miles per gallon (mpg). x 27 43 29 47 23
40 34 52 y 31 18 27 13 29 17 21 14 Complete parts (a) through (e),
given Σx = 295, Σy = 170, Σx2 = 11,617, Σy2 = 3950, Σxy = 5794, and
r ≈ −0.951. (a) Draw...

Do heavier cars really use more gasoline? Suppose a car is
chosen at random. Let x be the weight of the car (in
hundreds of pounds), and let y be the miles per gallon
(mpg).
x
27
46
30
47
23
40
34
52
y
30
20
25
13
29
17
21
14
Complete parts (a) through (e), given Σx = 299,
Σy = 169, Σx2 = 11,943,
Σy2 = 3861, Σxy = 5880, and
r ≈ −0.923.
(b) Verify...

Do heavier cars really use more gasoline? Suppose a car is
chosen at random. Let x be the weight of the car (in hundreds of
pounds), and let y be the miles per gallon (mpg). x 30 44 33 47 23
40 34 52 y 33 21 22 13 29 17 21 14 Complete parts (a) through (e),
given Σx = 303, Σy = 170, Σx2 = 12,123, Σy2 = 3950, Σxy = 6040, and
r ≈ −0.853.
(a) Draw...

Do heavier cars really use more gasoline? Suppose a car is
chosen at random. Let x be the weight of the car (in
hundreds of pounds), and let y be the miles per gallon
(mpg).
x
28
42
29
47
23
40
34
52
y
30
17
24
13
29
17
21
14
Complete parts (a) through (e), given Σx = 295,
Σy = 165, Σx2 = 11,587,
Σy2 = 3701, Σxy = 5650, and
r ≈ −0.945.
(a) Draw...

Professor wants to buy a new car, and of course it will be a
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trucks. The new system and the old system both produce about the
same average miles per gallon. However, engineers question which
system (old or new) will give better consistency in fuel
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A new fuel injection system has been engineered for pickup
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