1.10

(a) Identify the population of interest and the sample in this study. Population of interest was children/teenagers and the sample size was 160 individuals

(b) Comment on whether or not the results of the study can be generalized to the population, and if the findings of the study can be used to establish causal relationships. No they cannot as there is not enough informations, the group is not large and randomized enough (or it is not made evident). There could be a causal relationshio but it is unlikely unless if they are trying to establish it for that specific population.

1.20

(a) What type of study is this? Observational Study

(b) Can this study be used to conclude a causal relationship between increased stress and muscle cramps? No because they do not test other possible outcomes, there is no attempt to alter the result.

(c) State possible confounding variables that might explain the observed relationship between increased stress and muscle cramps. Decreased sleep and increased coffee consumption could have led to the cramps. They also didn’t take into account that during exams people tend to get less physical activity

1.30

(a) What type of study is this? Experiment

(b) Can this study be used to conclude a causal relationship between increased stress and muscle cramps? No because there are other factors that could cause cramps, such as the physical impact of being in an elevator thats falling down

save(Relationship, file = "Relationship.RData")
load(file = "Relationship.RData")
plot(Relationship$Stress,Relationship$Productivity,main = "Relationship between stress and productivity",xlab = "Stress",ylab = "Productivity")

1.50

  1. 2
  2. 3
  3. 1

1.60

  1. Symmetric
  2. Skewed to the Left
  3. Skewed to the right

1.70

(a) Based on the mosaic plot, is survival independent of whether or not the patient got a transplant? Explain your reasoning. No it appears as if survival was not independent of the transplant. From the data collected it indicates that patients lived longer if they got a transplant.

(b) What do the box plots below suggest about the efficacy (effectiveness) of the heart transplant treatment. The highest 25% of the control group lived less than the 75% of those who received transplants. This leads us to believe that the transplant does impact the survival time.

(c) What proportion of patients in the treatment group and what proportion of patients in the control group died? In the control group 30/34=0.8824 or 88.24% In the treatment group 45/69=0.6522 or 65.22%

(d) One approach for investigating whether or not the treatment is effective is to use a randomization technique.

i. What are the claims being tested? The first claim is that the transplant does not affect survival time, the second one would be that those who got a transplant were more likely to survive for longer than those who did not

ii. The paragraph below describes the set up for such approach, if we were to do it without using statistical software. Fill in the blanks with a number or phrase, whichever is appropriate.

We write alive on 28 cards representing patients who were alive at the end of the study, and dead on 75 cards representing patients who were not. Then, we shuffle these cards and split them into two groups: one group of size 45 representing treatment, and another group of size 30 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 100 times to build a distribution centered at 0. Lastly, we calculate the fraction of simulations where the simulated differences in proportions are ??. 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.

iii. What do the simulation results shown below suggest about the effectiveness of the transplant program? The results show that a difference of around 0.2302 (calculated as per the difference between deaths in control and treatment group) is unlikely to occur, therefore the initial hypothesis has to be rejected as transplants statistically improve the survival time.