Question

5. The total racetime for a 100-meter dash can be considered the sum of two variables: the reaction time to the starting signal and the running time for the 100 meters. The scatterplot shows reaction times and running times for 20 runners in a certain race. The winner was the runner with the least total race time. 11.0T 10.8 10.6 10.4 e10.2 100. 9.8 9.6 9.4 0.13 0.15 0.17 0.19 0.21 Reaction Time (seconds) Circle the point on the graph that represents the runner who won the race and approximate the total race time for that runner. (a) (b) Based on the graph, is it reasonable to assume that reaction time and running time are independent? Justify your answer (c) Based on the least-squares regression model created from the data, explain why the use of extrapolation to predict the running time for a runner whose reaction time is 0.30 second might not be appropriate.

Answer 1

a)

il tule least total race time. 11.0T 10.8 ︵ 10.6 10.4 10.2 10.0 9.8 9.6 9.4 0.13 0.15 0.17 0.19 0.21 Reaction Time (seconds)

The point encircled in red is the person who won the race, with the least running time and least reaction time.

b)

The scatter plot shows that there is a positive correlation between Reaction time and Running time. It is not correct to assume that the reaction time and running time are independent.

c) For this we need data.