Introduction

The data below was collected from a study involving 20 test subjects (UF Health). The goal was to determine if having two alcoholic drinks increases the average reaction time when driving. Test subjects drove an obstacle course before two drinks and had their reaction time recorded. After having two drinks, they drove the same course again and had their new reaction time recorded. The data for each test subject is listed below and arranged in order of fastest reaction time before two drinks to the slowest reaction time.

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

Distribution of Differences

This histogram shows the distribution of differences in reaction times in the order of reaction time after two drinks minus reaction time before two drinks. As shown in the histogram, the data is approximately normal.

Hypotheses

Using the data collected, a hypothesis test can be completed to see if there is enough evidence to show that there is an increase in reaction time after having two alcoholic drinks. The null and alternate hypotheses, where \(\mu_d\) represents the sample average of the difference between reaction time after and before two drinks, are presented below: \[H_o:\,\mu_d=0\] \[H_a:\,\mu_d>0\] Using these hypotheses, a two paired sample t-test will be conducted. The results of this test are given below:

## 
##  One Sample t-test
## 
## data:  afterminusbefore$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

Results Interpretation

Decision: Since p = 0.009 < alpha = 0.05, the null hypothesis gets rejected.

Conclusion: At 0.05 level of significance, there is enough evidence to show that having two alcoholic drinks increases the average reaction time while driving.

Works Cited

UF Health. (n.d.). Paired samples. Biostatistics. https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/