Introduction

This study aims to determine if drinking alcohol increases the average reaction times of drivers. Reaction times of a sample of 20 drivers were measured before and after drinking two beers. The mean reaction times are compared using a two-sample t-test for paired samples.

Sample Data

The table below shows the reaction times before and after the 20 subjects drank two beers. The difference between the before and after values also is shown in the column labeled “AfterMinusBefore”.

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

Normality in the Sample of Differences

Normality in the sample of differences is checked with a histogram and a QQ plot. The histogram below shows that the shape of the distribution is fairly normal, although it may be bimodal.

Normality of the distribution can be seen more clearly in the following QQ plot.

Hypotheses

A two-sample t-test for paired samples is conducted to test the null hypothesis that the mean difference in reaction times is zero. The null and alternative hypotheses are expressed below:

\[H_0:\mu=0\] \[H_a:\mu\gt 0\]

Results

The results of the t-test are shown below.

## 
##  Paired t-test
## 
## data:  allInfo$After and allInfo$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

The p-value is .0087, so the null hypothesis is rejected.

Conclusion

At the .05 level of significance, on average, there is sufficient evidence to conclude that driver reaction times increase after drinking two beers.

Works Cited

UF Biostatistics. “Open Learning Textbook.” Paired Samples, n.d., https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/