In this study we will be looking at the reaction time of sober drivers, then the reaction time of drivers after 2 beers.

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

## 
##  Paired t-test
## 
## data:  B2B_A2B_Combined$After and B2B_A2B_Combined$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

\[H_0:\,\mu_d=0\]

\[H_a:\,\mu_d>0\]

The histogram was normally distributed which shows the normality is met.

Also since the P-value is below 0.05 we reject the null hypothesis

According the results seen and given in the paired two sample t-test, there is good enough evidence to say that the mean after the results is more than the mean before the results