Assignment Direction 1

##   SubjectID Before
## 1         2   2.96
## 2        13   3.16
## 3         4   3.94
## 4        16   4.05
## 5        17   4.42
## 6        20   4.69
##   SubjectID After
## 1        12  7.23
## 2         1  6.85
## 3        14  6.42
## 4        11  6.25
## 5         7  6.09
## 6        19  6.03

Assignment Direction 2

##    SubjectID Before After
## 1          2   2.96  4.78
## 2         13   3.16  4.55
## 3          4   3.94  4.01
## 4         16   4.05  5.59
## 5         17   4.42  3.96
## 6         20   4.69  3.72
## 7          6   4.81  5.34
## 8          5   4.85  5.91
## 9         10   4.88  5.75
## 10         3   4.95  5.57
## 11        18   4.99  5.93
## 12        19   5.01  6.03
## 13         9   5.15  4.19
## 14        12   5.26  7.23
## 15         8   5.33  5.84
## 16        15   5.49  5.25
## 17        11   5.75  6.25
## 18         1   6.25  6.85
## 19         7   6.60  6.09
## 20        14   6.65  6.42

Joining the Before and After columns by Subject ID

Assignment Direction 3

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

Though our sample size is small, there is no indication from our sample that our population is not normal. If it did, our test would be unreliable.

Histogram

In our histogram, the data represents the sample of differences (After - Before) from the AfterMinusBefore column. From this, we can see that our histogram is approximately normally distributed as we maintain a bell-shaped curve.

QQ-Plot

The QQ-plot also represents the sample of differences from the AfterMinusBefore column. It maintains all of it’s points within the envelope making it also approximately normally distributed.

Both the histogram and QQ plot show normality. With the histogram, we can tell it is approximately normal because of it’s bell shaped curve. With the QQ plot, we can tell it is approximately normal because the points fall within the line or within the envelope. Both the histogram and the QQ-plot having normality from the sampling distribution allows us to make the conclusion that the population may also be normally distributed.

Assignment Direction 4

Null Hypothesis:

\[H_0:\mu=0\] Alternative Hypothesis:

\[H_a:\mu>0\]

Assignment Direction 5

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

Decision: p-value is less than 0.05. We reject the null hypothesis

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

Work Cited:

“Paired Samples.” University of Florida Biostatistics Open Learning Textbook. https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/.