Report 2 is about the understanding of normality, t-test, and how this can reject or acceptation the null hypothesis of something. It is about the different reactions times of people before and after 2 drinks. This data set can help us determine whether we reject or accept the null hypothesis.

Distribution

A part of running tests on data is to check and find the Distribution type of the data. You most check to see if the distribution type is normal or has normality. This data sample size is not that large we need to check the distruption with a histagram.

Looking at the histgram, you can see that the data is approximately normally distributed. Although at first with the wrong number of bins this data set will look adnormally disributed. With the right number of bins it is clealy normally distributed.

Looking at the histgram, you can see that the data is approximately normally distributed. Although at first with the wrong number of bins this data set will look adnormally disributed. With the right number of bins it is clealy normally distributed.

Beers Reaction Test

After joining the two dara sets of before and after and adding the new column. You can see the data that shows that your reaction time gets slower after two beers. The t-test and hypotheses are below. We are testing the following hypotheses:

\[ H_0: \mu = 0 \]

\[ H_a: \mu > 0 \]

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

Note that the echo = FALSE parameter was added to the code chunk to prevent printing of the R code that generated the plot.

Decision

With a p-value of 0.008734, it is much smaller than alpha value of 0.05. So the P is small so we should reject the null hypothesis.

Conclusion

At a 0.05 level of significance there is enough evidence that drinking 2 beers does make your raction time slower.

Work Citied

https://bolt.mph.ufl.edu/6050-6052/unit-4b/module-13/paired-t-test/