Reference no: EM13583349

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.