Effect of Alcohol on Drivers’ Reaction Times

Does alcohol intake increase the reaction time of a driver? In this report, I will analyze reaction times of 20 drivers as recorded before and after they had two beers. The table below contains the reaction times and their differences.

SubjectID Before After AfterMinusBefore
2 2.96 4.78 1.82
13 3.16 4.55 1.39
4 3.94 4.01 0.07
16 4.05 5.59 1.54
17 4.42 3.96 -0.46
20 4.69 3.72 -0.97
6 4.81 5.34 0.53
5 4.85 5.91 1.06
10 4.88 5.75 0.87
3 4.95 5.57 0.62
18 4.99 5.93 0.94
19 5.01 6.03 1.02
9 5.15 4.19 -0.96
12 5.26 7.23 1.97
8 5.33 5.84 0.51
15 5.49 5.25 -0.24
11 5.75 6.25 0.50
1 6.25 6.85 0.60
7 6.60 6.09 -0.51
14 6.65 6.42 -0.23

There are only 20 data points. Therefore, we have to verify that the data is normally distributed before proceeding with the test. We can use a histogram to analyze the distribution.

From the histogram above, we can see that the data is normally distributed. Additionally, from the qqplot below, every data point falls in the 95% confidence band indicating that the data is normally distributed.

We’ll start by stating the null and alternative hypotheses for our test. \[H_0: \mu=0\] \[H_a: \mu>0\] I will now run a paired sample t-test for the data.

## 
##  One Sample t-test
## 
## data:  joined_table$AfterMinusBefore
## t = 2.6031, df = 19, p-value = 0.008734
## alternative hypothesis: true mean is greater than 0
## 95 percent confidence interval:
##  0.1690516       Inf
## sample estimates:
## mean of x 
##    0.5035

As we can see, the t-score is 2.6031 which gives a p-value of 0.008734.

Decision

\[p < \alpha \ \ \ \ \therefore\ \ we \ \ reject \ \ the \ \ null\]

Conclusion

At a 0.05 level of significance, there is enough evidence to conclude that there is an increase in the average reaction times of drivers after alcohol intake.