Before and After Two Beers

Before and After Drinking Two Beers

This an analysis of data taken from participants in a study of reaction time before and after drinking two beers. The table below is the data for the subjects. The table displays the times before two beers, after two beers and the difference between the reaction times. The null hypothesis claims there would not be a statistical difference in reaction time after drinking two beers.\[H_0:\,\mu_d=\mu_0\] The alternative hypothesis claims there would be a difference in reaction time.\[H_a:\,\mu_d≠0\] We will be conducting a two sided paired t-test to determine the results.

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

From the table above, the average before reaction was \(\mu_b\)=4.9595 and the average after reaction was \(\mu_a\)=5.463. The change in reaction time with the current subjects would have a normal distribution. The graph below shows this.

As stated, we have conducted a two sided paired t-test and the results are listed below.

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

The \(p\)=0.008734 < \(\alpha\)=0.5. The P-Value is small so we reject the null hypothesis. At \(\alpha\) of 0.05 level of significance, there is enough evidence to conclude the reaction time increased after the consumption of two beers.

Before and After Two Beers

James Hanson

2024-11-21

Before and After Drinking Two Beers

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