Rickidon Singh, Data 606 HW1 (Chapter 1 problems- OpenIntro Statistics 3rd Ed. )

Q1.8 Smoking habits of UK residents.

(a) What does each row of the data matrix represent?

Each row represents a case, data from one individual

(b) How many participants were included in the survey?

Total participants that were included: 1,691

(c) Indicate whether each variable in the study is numerical or categorical. If numerical, identify as continuous or discrete. If categorical, indicate if the variable is ordinal.

sex- Categorical Variable

marital- Categorical Variable

smoke- Categorical Variable

age- Numerical Continuous Variable

gross income- Numerical Discrete

amtWeekends- Numerical Discrete

amtWeekedays- Numerical Discrete

Q1.10 Cheaters, scope of inference.

(a) Identify the population of interest and the sample in this study.

Children are the population of interest between 5 and 15 years old. The sample size is 160.

(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.

Since we are unaware whether or not the sample was chosen randomly, the results can’t be genearlized. Casual relationships can’t be established since the sample population is mainly partiipants.

Q1.28 Reading the paper. Below are excerpts from two articles published in the NY Times:

(a) An article titled Risks: Smokers Found More Prone to Dementia states the following: “Researchers analyzed data from 23,123 health plan members who participated in a voluntary exam and health behavior survey from 1978 to 1985, when they were 50-60 years old. 23 years later, about 25% of the group had dementia, including 1,136 with Alzheimer’s disease and 416 with vascular dementia. After adjusting for other factors, the researchers concluded that pack-aday smokers were 37% more likely than nonsmokers to develop dementia, and the risks went up with increased smoking; 44% for one to two packs a day; and twice the risk for more than two packs.” Based on this study, can we conclude that smoking causes dementia later in life? Explain your reasoning.

Based on this study, we can’t conclude that dementia is caused by smoking since the sample wasn’t random. As a suggestion, other factors such as alcohol abuse and genetics should’ve been looked at as well.

(b) Another article titled The School Bully Is Sleepy states the following: “The University of Michigan study, collected survey data from parents on each child’s sleep habits and asked both parents and teachers to assess behavioral concerns. About a third of the students studied were identified by parents or teachers as having problems with disruptive behavior or bullying. The researchers found that children who had behavioral issues and those who were identified as bullies were twice as likely to have shown symptoms of sleep disorders.” A friend of yours who read the article says, “The study shows that sleep disorders lead to bullying in school children.” Is this statement justified? If not, how best can you describe the conclusion that can be drawn from this study?

I don’t think this statement is justified because this would be considered an observational study as opposed to a true experiment since this wasn’t a random experiment. One can say that both are co-related, where lack of sleep can increase the chance of bullying.

Q1.36 Exercise and mental health. A researcher is interested in the e↵ects of exercise on mental health and he proposes the following study: Use stratified random sampling to ensure representative proportions of 18-30, 31-40 and 41- 55 year olds from the population. Next, randomly assign half the subjects from each age group to exercise twice a week, and instruct the rest not to exercise. Conduct a mental health exam at the beginning and at the end of the study, and compare the results.

(a) What type of study is this?

This study is an experiment

(b) What are the treatment and control groups in this study?

The group which is instructed to excercise is the treatment group and the control group is the group who is refrained from excercising.

(c) Does this study make use of blocking? If so, what is the blocking variable?

Yes, this study makes use of blocking based on age.

(d) Does this study make use of blinding?

No, this study doesn’t make use of blinding.

(e) Comment on whether or not the results of the study can be used to establish a causal relationship between exercise and mental health, and indicate whether or not the conclusions can be generalized to the population at large.

Yes, a casual link can be made from this study however, and the results can be generalized since there is a random samplilng and random assignments.

(f) Suppose you are given the task of determining if this proposed study should get funding. Would you have any reservations about the study proposal?

This is a good study however, I would make some suggestions. For one, the study should have both groups examined multiple times throughout the study instead of only twice. Also, measuring compliance would be another suggestion.

Q1.48 Stats scores. Below are the final exam scores of twenty introductory statistics students. 57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94. Create a box plot of the distribution of these scores.

scores <- c(57, 66, 69, 71, 72, 73, 74, 77, 78, 78, 79, 79, 81, 81, 82, 83, 83, 88, 89, 94)
boxplot(scores)

summary(scores)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   57.00   72.75   78.50   77.70   82.25   94.00

Q1.50 Mix-and-match. Describe the distribution in the histograms below and match them to the box plots.

a.Symmetrical distributed, (box plot 2)

b.Uniformly distributed, (box plot 3)

c.Right Skew distributed, (box plot 1)

Q1.56 Distributions and appropriate statistics, Part II . For each of the following, state whether you expect the distribution to be symmetric, right skewed, or left skewed. Also specify whether the mean or median would best represent a typical observation in the data, and whether the variability of observations would be best represented using the standard deviation or IQR. Explain your reasoning.

(a) Housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000.

This is a Right skewed distribution. Median is $450,000 and a good amount of homes are above $6,000,000

(b) Housing prices in a country where 25% of the houses cost below $300,000, 50% of the houses cost below $600,000, 75% of the houses cost below $900,000 and very few houses that cost more than $1,200,000.

This is a Symmetric distribution and would use the mean and standard deviation as indicators.

(c) Number of alcoholic drinks consumed by college students in a given week. Assume that most of these students don’t drink since they are under 21 years old, and only a few drink excessively.

This is a Right skewed distribution and would use median and IQR as indicators.

(d) Annual salaries of the employees at a Fortune 500 company where only a few high level executives earn much higher salaries than the all other employees.

This is a Right skewed distribution with a lot of outliers and would use median and IQR as indicators.

Q1.70 Heart transplants. The Stanford University Heart Transplant Study was conducted to determine whether an experimental heart transplant program increased lifespan. Each patient entering the program was designated an official heart transplant candidate, meaning that he was gravely ill and would most likely benefit from a new heart. Some patients got a transplant and some did not. The variable transplant indicates which group the patients were in; patients in the treatment group got a transplant and those in the control group did not. Another variable called survived was used to indicate whether or not the patient was alive at the end of the study.

(a) Based on the mosaic plot, is survival independent of whether or not the patient got a transplant? Explain your reasoning.

No, survival isn’t independent of whether or not the patient got a transplant

(b) What do the box plots below suggest about the efficacy (e↵ectiveness) of the heart transplant treatment.

The box plots are suggesting that the heart transplant will increase the survival rate.

(c) What proportion of patients in the treatment group and what proportion of patients in the control group died?

Control Group:

(30/34 *100) = 88% patients died

Treatment Group:

(45/69 * 100) = 65% patients died

(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?

Claim being tested is that a heart transplant will increase longevity for a very sick patient.

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 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 100 times to build a distribution centered at 0. Lastly, we calculate the fraction of simulations where the simulated difference in proportions are less than or equal to -0.230179. 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 are suggestive for the transplant program’s effectiveness since the difference between the 100 simulations is centered near 0. The heart transplant improves survival rate.