Executives at Toyota were given the new high-performance 3.5-litre V6 SUV automobile, they were asked to keep records of the number of miles travelled per gallon of petrol for this new vehicle using regular petrol versus high octane petrol. Their results follow. Miles per gallon High Executive Regular Octane Bowers 25 28 Smith 33 31 Grasser 31 35 Jones 45 44 BUD 42 47 Rau 38 James 29 Burns 42 Snow 41 Lawless 30 Perform a dependent samples t-test (paired t-test) to examine if there is a difference in the number of miles travelled per gallon. Use a 5% significance level. (a) State the null hypothesis and the alternate hypothesis. (2 Marks) (b) Compute the value of the test statistic. (state your answer accurate to 2 decimal places) Test Statistic ( = (2 Marks) (c) State the Degrees of Freedom? df = (2 Marks) (d) Look up the critical value to (state to 3dp as given in your t-tables) (2 Marks) (e) Ho. There is v evidence to indicate that there is a difference in the miles per gallon between the two types of petrol