Part 2

Problem 1:

2.1 a.
rosi <- 2593/ 67593 
pio <- 5386 / 159978
rosi
## [1] 0.03836196
pio
## [1] 0.03366713

FALSE. I divided the patients who have cardiovascular problems and took rosiglitazone with the respective total and got 0.384. I also took the patients who had cardiovascular problems and took pioglitazone and divided it by the respective total and got 0.0337. We can see that the rate of cardiovascular problems for those on rosiglitazone is higher.

2.1 b.

TRUE. We can see that diabetic patients who are taking rosiglitazone are more likely to have cardiovascular problems.

2.1 c.

FALSE. We cannot draw a casual conclusion from the data by itself.

2.1 d.

TRUE. We may need to run an experiment.

Problem 2:

2.2 a.
45/69
## [1] 0.6521739

The Proportion of patients in the treatment group that died

30/34
## [1] 0.8823529

The proportion of patients in the control group that died

2.2 b i.

H0: There is no difference in death rates between the control and treatment group.

HA: There is a difference in death rates between the control and treatment group.

2.2 b ii.

We write alive on 28 cards representing who were alive at the end of the study, and dead on 75 cars representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size 69 representing treatment, and another group of size 34 representing control. We calculate the difference between the proportion of dead cards in the treatment and control groups (treatment - control) and record this value. We repeat this many times to build a distribution centered at 0. Lastly, we calculate the fraction of simulations where the simulated differences in proportions are -0.23. If this fraction is low, we conclude that it is unlikely to have observed such an outcome by chance and that the null hypothesis should be rejected in favor of the alternative.

2.2 b iii.

The simulation results suggest that the proportions are normally distributed. Also, the null should be rejected.

Problem 3:

2.4 a.

This is a randomized control experiment.

2.4 b.

Yes, this study makes use of blinding because half of the participants who received a placebo pill did not know that they recieved the placebo pill.

2.4 c.
Panti <- 66/85
Pplac <- 65/81
Panti
## [1] 0.7764706
Pplac
## [1] 0.8024691
Panti - Pplac
## [1] -0.02599855
2.4 d.

At first glance, the placebo pill seems to be more effective because the proportion of the placebo was bigger.

2.4 e.

H0: There is no impact in improvement between the antibiotic and placebo pill.

HA: There is an impact in improvement between the antibiotic and placebo pill.

2.4 f.

In this experiment, we fail to reject the null because there is no impact between the antibiotic and placebo pill. We can see from the histogram that 66 falls under the normal distribution curve, so it is not unusual.