At an athletics meet, organisers were interested in whether the standard of the competitors running in the 400m event varied significantly between heats. There were four heats for the 400m event, with 6 competitors in heats 1 and 3, 8 runners in heat 2 and 7 in heat 4. The time (in seconds) each runner took to complete the event was recorded, with the data given in the following table.

Heat

1 2 3 4

51.92 53.25 53.10 51.22

51.29 52.17 53.20 50.11

52.90 53.10 53.12 51.19

52.97 51.53 52.96 50.34

52.10 54.22 53.91 51.78

51.89 52.85 52.55 52.25

54.17 51.22

54.58

a)State the null and alternative hypotheses required to test if the average 400m running times were significantly different between any of the heats.

b)Carry out the ANOVA (with technology) and report the test statistic and P-value.

c)Write a brief conclusion of the ANOVA analysis, in context. Use = 0.05.

d)Carry out the Bonferroni's multiple comparisons (if appropriate) and summarise the results.