I need help finding the test statistic and whether to reject/fail to reject the

Question

I need help finding the test statistic and whether to reject/fail to reject the null.

A car dealer is interested in comparing the average gas mileages of four different car models. The dealer believes that the average gas mileage of a particular car will vary depending on the person who is driving the car due to different driving styles. Because of this, he decides to use a randomized block design. He randomly selects five drivers and asks them to drive each of the cars. He then determines the average gas mileage for each car and each driver. Can the dealer conclude that there is a significant difference in average gas mileages of the four car models? The results of the study are as follows Car ACar B Car C Car D Driver 130 39 Driver 2 21 Driver 3 30 36 28 Driver 4 26 262 Driver 5 38 36 37 38 31 28 36 40 28 ANOVA df MS Source of Variation Rows Columns Error 297.8000 474.4500 148.5500 349.5167 202.2000 1216.8500 648.5500 19

Explanation / Answer

The test statistics are calculated as the following tables

Test statistic: Drivers(rows) F =74.45 /16.85 = 4.418

Here F-value of Drivers (rows) =  4.41898 > F - critical value ,3.259167, at 5% and (4,12) df

So We reject H0

Thus we conclude that there is significance difference among the means of drivers

Test Statistic: Cars(Column) F =49.5166 /16.85 = 2.9386

Here F-value of Cars(column) =  4.41898 < F - critical value ,3.4902, at 5% and (3,12) df

So We do not reject H0

Thus we conclude that there is no significance difference among the means of cars

Source df Sum of square mean Square F F-critical Rows 4 297.8 74.45 4.418398 3.259167 Columns 3 148.55 49.51666667 2.938675 3.490295 Error 12 202.2 16.85 Total 19 648.55

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