A paired t-test was conducted to evaluate whether alcohol consumption increases average reaction times in drivers. The analysis used two datasets: one containing reaction times of sober drivers and another with the reaction times of the same drivers after consuming two beers. As we can see below the datasets were combined and prepped for analysis by calculating the differences in reaction times for each participant.

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

The sample size is not large (n = 20), so in order to proceed, we need to look at the histogram to make sure there is no evidence that the normality assumption is not met. As we can see in the histogram below, there is no evidence of violation of the normality assumption.

NULL AND ALTERNATIVE HYPOTHESIS

## Null Hypothesis (H₀): after = before
## Alternative Hypothesis (H₁): after > before

T-TEST

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

DECISION

## p-value = 0.008734 < α = 0.05 (level of significance)
## Reject the null hypothesis

CONCLUSION

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

Works Cited:

“Paired t-Test.” Biostatistics Online Learning Tools. Accessed 20 Nov. 2024. https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/.