Introduction

Drunk driving contributes to 31% of all traffic related deaths in the United States. There seems to be a common misconception that 1-2 drinks cannot get you drunk. We have been given two data sets of 20 individuals taking a reaction time test. The first data set is before the subjects consumed 2 beers and the second data set is after the subjects consumed two beers. We have combined those data sets into our data frame listed below with the addition of a calculated field taking the difference of the participants reaction time after the beers and before the beers.

Data Frame

## Rows: 20 Columns: 2
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ","
## dbl (2): SubjectID, Before
## 
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.
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

Our sample size for this study is 20 individuals which is considered small so in order to promote research integrity we are attempting to show that the population of differences approximately resembles the normal distribution as seen in the histogram below.

Histogram

Hypotheses

Our null hypothesis is \[H_0:\,\mu_d=0\] and our alternative hypothesis is \[H_a:\,\mu_a>0\]

## 
##  Paired t-test
## 
## data:  a and b
## 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

Decision

Our student-t’s test statistic is 2.6031 which means that the sample mean is 2.6031 standard errors away from the null hypothesis and our p-value is 0.008734 which is statistically significant. Our p value .008734 is smaller than our significance level of .05 therefore we reject the null hypothesis.

Conclusion

Our p-value is 0.008734 which at a significance level of .05 there is enough evidence to reject the null hypothesis. There is enough evidence that drinking two beers is associated with a longer reaction time in car drivers.

##Works cited

https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/ (Source for data sets)
https://www.thezebra.com/resources/research/drunk-driving-statistics/ (drunk driving statistics)