Introduction

A study was conducted to see if drivers were affected after drinking two beers. The study used a random sample of 20 drivers. Each driver’s reaction time was measured before and after they drank the two beers. The table below shows the reaction times of each driver before and after they drank the beers as well as the difference in their reaction time (after-before).

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

Histogram

The histogram below includes the difference in reaction time for after minus before for each individual. Because the sample size of 20 is small, we need to look at the normality of the distribution of differences. Looking at this histogram there is no indication that the population is not normal. With this information we are able to conduct a t-test to help determine if the data suggests an increase in the average reaction time after the drivers drank two beers.

T-Test

For our t-test: Null hypothesis: \(H_0: \mu_d=0\) Alternative hyothesis: \(H_a: \mu_d>0\)

## 
##  Paired t-test
## 
## data:  calculatedtable$After and calculatedtable$Before
## t = 2.6031, df = 19, p-value = 0.008734
## alternative hypothesis: true mean difference is greater than 0
## 95 percent confidence interval:
##  0.1690516       Inf
## sample estimates:
## mean difference 
##          0.5035

Decision

Since \(p=0.008734\) < \(\alpha=0.05\) we reject the null hypothesis.

Conclusion

At a significance level of \(\alpha=0.05\) we have enough evidence that the average reaction time after the alcohol intake increased.

Works Cited

https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/