Introduction

The focus of this report is on the reaction time of sober drivers versus the reaction time of drivers who have consumed two beers. There are two separate data sets that are used for this analysis in which one contains data before drinking the alcoholic beverages and the other contains data after drinking the two beers. The goal of this report is to determine if there is enough evidence to say the difference in reaction time is caused by the alcohol consumption. We will use a t-test for paired samples to come to this conclusion.

To prepare the data set, we must first join the two tables and create a column computing the difference between the reaction times of before and after drinking the beers. This will allow us to run the t-test for paired samples.

Normality Check

After joining the two tables and adding a difference column of After Minus Before, we need to confirm that the sample is normally distributed because normality confirms valid results of the t-test. Therefore, a histogram is provided to show the distribution of the data.

The histogram has a nice bell curve which means that the sample passes the normality check. We can continue on to the t-test.

Two-Sample T-Test For Paired Samples

\[H_0:mu{}=0.5035\] \[H_a:mu{}<0.5035\]

## 
##  Paired t-test
## 
## data:  Combined_Table_df$Before and Combined_Table_df$After
## t = -2.6031, df = 19, p-value = 0.9913
## alternative hypothesis: true mean difference is greater than 0
## 95 percent confidence interval:
##  -0.8379484        Inf
## sample estimates:
## mean difference 
##         -0.5035

Decision & Conclusion

P = 0.9913 > 0.05. P is not small, do not reject the null. At a level of significance of 0.05, there is not enough evidence indicating the reaction time of an individual with two beers in their system is slower than a individual with no beer in their system.

Work Cited

University of Florida. Paired t-test. University of Florida, n.d., bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/. Accessed 19 Nov. 2024.