Introduction

This report looks at the reaction times of drivers before and after drinking two beers. The goal is to find out whether alcohol intake significantly increases average reaction time.

Data Preparation

We join the two datasets by SubjectID so each driver’s before and after times are side by side.

##   SubjectID ReactionTime_Before ReactionTime_After
## 1         2                2.96               4.78
## 2        13                3.16               4.55
## 3         4                3.94               4.01
## 4        16                4.05               5.59
## 5        17                4.42               3.96
## 6        20                4.69               3.72

Table 1 above presents the combined reaction time measurements for a sample of drivers. Each row shows an individual driver’s reaction time before and after consuming two beers.

Hypotheses

\[H_0:\; \mu = 0\]
\[H_1:\; \mu > 0\]

Results

Figure 1 shows that the differences are approximately normally distributed, supporting the use of a paired t-test. The distribution appears almost symmetric and bell-shaped, with most differences clustering between -1 and 2 seconds.

A paired t-test was conducted on 20 subjects,with a mean difference of 0.5035 and a standard deviation of 0.86. The test produced a t-statistic of 2.60 and a p-value of 0.0087, indicating that drivers reaction times increased after consuming two beers.

Decision

Since P value is less than 0.05 , we reject the null hypothesis

Conclusion

At the 0.05 level of significance, there is sufficient evidence to conclude that the mean reaction time of drivers significantly increased after consuming two beers.

Works Cited

“Paired Samples.” Biostatistics, web.archive.org/web/20220519220227/https:/bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/. Accessed 12 Dec. 2025.