|
Car Size (m^3)
|
Body
|
Year
|
Year
|
|
9.941
|
Small Cars
|
2003
|
Less than 2005
|
|
10.251
|
Small Cars
|
1996
|
Less than 2005
|
|
10.699
|
Small Cars
|
2012
|
Greater than 2005
|
|
9.139
|
Medium Cars
|
1972
|
Less than 2005
|
|
10.426
|
Medium Cars
|
1986
|
Less than 2005
|
|
11.304
|
Medium Cars
|
2001
|
Less than 2005
|
|
12.255
|
Medium Cars
|
2007
|
Greater than 2005
|
|
12.332
|
Medium Cars
|
2007
|
Greater than 2005
|
|
13.305
|
Large Cars
|
2004
|
Less than 2005
|
|
13.387
|
Large Cars
|
2004
|
Less than 2005
|
|
13.955
|
Large Cars
|
2004
|
Less than 2005
|
|
13.402
|
Large Cars
|
2011
|
Greater than 2005
|
|
13.470
|
Large Cars
|
2011
|
Greater than 2005
|
|
13.484
|
Large Cars
|
2010
|
Greater than 2005
|
|
14.618
|
Luxury Cars
|
2010
|
Greater than 2005
|
|
14.987
|
Luxury Cars
|
2010
|
Greater than 2005
|
|
13.814
|
Luxury Cars
|
2002
|
Less than 2005
|
|
14.278
|
Luxury Cars
|
2002
|
Less than 2005
|
Use Minitab to test if your numerical variable has the same true mean for the different levels of your 3+ level categorical variable.
a) Write down the null and alternative hypotheses to examine this question using ANOVA.
b) Assumption checking:
(i) State the assumptions for the ANOVA test.
(ii) Use Mintab to check whether these assumptions are valid for your data. (Hint: use Normal Probability Plots, compare the sample standard deviations and comment on independence).
(iii) Discuss whether your data needs transforming. If a transformation is needed, select a suitable transformation and transform your data.
c) Use Minitab to carry out the ANOVA on your (transformed if necessary) data.
(i) State the test statistic and corresponding p-value.
(ii) Explain whether you have evidence for or against the null hypothesis.
(iii) State your conclusion in a form that a non-statistician would understand.