Texting and Driving: A Study on Driver Reaction Time

In a 2011 study from Texas A & M University, forty-two drivers were placed behind the wheel of a car and drove around a closed track about 11 miles in length. The researchers monitored how long it took drivers to react to a flashing light while driving normally and while attempting to text or to read a message on a mobile phone. Here is a summary of the data.

standard conditions # observations mean deviation control 42 1.754 0.806 texting 42 4.302 1.614 reading 42 3.278 1.274

a. Give the appropriate hypothesis for this situation. Clearly define any parameters used. b. Show the hand calculation of the F statistic for a one way analysis of variance. Include the details for the SSB, SSR, DFB, DFR. Organize this process in the table, AND show the by-hand work for SSB, SSR, DFB, DFR, and F

a. The appropriate hypothesis for this situation is:

H0: μ1 = μ2 = μ3 (There is no difference in mean reaction time between standard conditions, texting, and reading conditions) Ha: At least one mean reaction time is different from the others.

Where: μ1 = population mean reaction time under standard conditions μ2 = population mean reaction time while texting μ3 = population mean reaction time while reading

b.

Source | SS | df | MS | F -------|----|----|----|-- Between | SSB | 2 | MSB = SSB/2 | F = MSB/MSW Within | SSR | 123 | MSW = SSR/123 | Total | SST | 125 | |

SSB = [(1.754 - 3.611)^2 x 42] + [(4.302 - 3.611)^2 x 42] + [(3.278 - 3.611)^2 x 42] = 113.306

DFB = k - 1 = 3 - 1 = 2

MSB = SSB/DFB = 113.306/2 = 56.653

SSR = [(1-1.754)^2 + (1-1.754)^2 + ... + (1-4.302)^2 + ... + (1-3.278)^2] + [(1-1.754)^2 + ... + (1-3.278)^2] + [(1-4.302)^2 + ... + (1-3.278)^2] = 460.554

DFR = N - k = 126 - 3 = 123

MSW = SSR/DFR = 460.554/123 = 3.742

F = MSB/MSW = 56.653/3.742 = 15.131

The calculated F statistic is 15.131.