Question

Question 4

Researchers studied four different blends of gasoline to determine their effect on miles per gallon (MPG) of a car. An experiment was conducted with a total of 28 cars of the same type, model, and engine size, with 7 cars randomly assigned to each treatment group. The gasoline blends are referred to as A,B,C, and D.The MPGs are shown below in the table

Gasoline Miles Per

Blend Gallon

A 26 28 29 23 24 25 26

B 27 29 31 32 25 24 28

C 29 31 32 34 24 28 27

D 30 31 37 38 36 35 29

We want to test the null hypothesis that the four treatment groups have the same mean MPG vs. the alternative hypothesis that not all of the means are equal.

a) Before carrying out the analysis, check the validity of any assumptions necessary for the analysis you will be doing. Write a brief statement of your findings

b) Test the null hypothesis that the four gasoline blends have the same mean MPGs, i.e., Test Ho: ua=ub=uc=ud vs. the alternative hypothesis Ha: not all the means are equal.

c) If your hypothesis test in (b) indicates a significant difference among the treatment groups, conduct pairwise multiple comparison tests on the treatment group means. Underline groups of homogeneous means.

d) Briefly state your conclusions.

( Use IBM SPSS for all calculations)

Answer 1

a) One way ANOVA is applied for the analysis and the underlying principle of anova are

1. The values are simple random samples and they need to be independent samples.
2. The underlying populations should be normally distributed. However, the ANOVA test is robust and moderate departures from normality aren’t a problem

b) Consider the hypothesis

Ho: ua=ub=uc=ud

v/s.

Ha: not all the means are equal.

From the one way ANOVA we have the p value as p.value=0.0006306

Which says to reject the null hypothesis and to conclude that there exist a significant difference among the treatment groups.

c) On conducting pairwise multiple comparison test i.e pairwise t test after applying one way ANOVA the group of homogeneous means were found as A,B and C

d) The following Conclusions were made from pairwise multiple comparison test

The difference in means of B and C is less than 0

The difference in means of A and D is significant

The difference in means of A and B is less than 0