### Hypothesis test for two factors anova

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Hypothesis test for two factors ANOVA.

A mail order catalogue company operates with three distinct models of delivery vehicle. These are also available in two engine sizes (2.2 litre and 2.6 litre). The logistics manager believes that it would substantially reduce maintenance costs if only one model with a single engine size were used when replaing the fleet. Five vehicle sfor each combination of model type and engine size were randomly selected and the average distance travelled before receiving necessary maintenance, over previous year, was recorded for each. A 2-way ANOVA with interaction was then conducted on these data and the results of this are exhibited in table. Several of the values are missing in this table. You may assume that all model assumptions hold.

a) Provide the missing valuein table. You must show how you have calculated these values.

b) State your conclusions for the ANOVA from the resulting ANOVA table. You must state H0 and H1 for each test that conduct and provide a clear statement of your conclusions for the tests. You must also state your overall findings, assuming that the model assumptions are satisfied.

c) The Cook's Distances obtained from the fitted model are exhibited graphically in figure. Explain what thses represent and, based on figure, whether there is a problem with the data r otherwise.

 Source Degrees of freedom SS MSS F P-value Model 2 84218884 MSSM 562.91 <0.0001 Engine size 1 SSES 294990 3.94 0.059 Interaction df1 296716 MSSI 1.98 0.160 Errors 24 SSE 74807 - - Total dfT 86605953 - - -

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