Question 2 [21 marks] The 100 metre Sprint is one of the most watched events in any Olympic Games. Sprinters

will often go to great lengths to improve their times, looking into factors such as the

equipment they use and the coaches they hire. Listed in the table below are the personal

best times for the 100 metre sprint for 27 sprinters that are in training. The 27 sprinters

were chosen as follows: For each of three shoe brands (the Fast, the Quick and the

Speedy brand), 9 sprinters who used that particular brand were randomly selected. The

sample variances of the times for each shoe brand are also listed in the table. Shoe Brand Times 32 Fast 9.82 10.22 10.15 9.77 10.12 9.86 9.87 10.11 10.18 0.0313111

Quick 9.67 9.95 10.10 10.16 9.98 10.09 10.20 10.68 10.29 0.0753278

Speedy 9.69 9.75 9.49 10.03 9.66 10.24 10.04 9.87 10.01 0.0557528 (a) [6 marks] Test whether the mean time for sprinters using the speedy brand is more

than 0.2 seconds faster than for sprinters using the quick brand. Clearly state your

hypotheses and use a signiﬁcance level of a = 5%. Clearly state any assumptions

you have made (without testing them) when performing this test. A one-way AN OVA was performed on this data, using shoe brand as the factor. The

partially ﬁlled ANOVA table is provided below: (b) [2 marks] Calculate the sum of squares for error for the one-way ANOVA.