The following problems are copied from the chapter 2 exercises from Introduction to Modern Statistics First Edition by Mine Çetinkaya-Rundel and Johanna Hardin (https://openintro-ims.netlify.app/data-design.html)

chapter 2 exercise

  1. Music and learning. You would like to conduct an experiment in class to see if students learn better if they study without any music, with music that has no lyrics (instrumental), or with music that has lyrics. Briefly outline a design for this study.

ANSWER: We would use a simple random sample, first I would take a 6 sided dice and roll it for each student in the class . 1 and 2s would be assigned the without music treatment, 3s and 4s would be assigned the music without lyrics treatment, and 5s and 6s would be assigned the music with lyrics treatment. After a week of said treatment an exam would be assigned on the subject they were studying and we would see which group did the best or if there is no statistical significance.

  1. Exercise and mental health. A researcher is interested in the effects of exercise on mental health, and they propose 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.
  1. What type of study is this?

ANSWER: Randomized Experiment

  1. What are the treatment and control groups in this study?

ANSWER: Control groups are the half of each age group that were told not to exercise. Treatment groups are the half of each age group that were told to exercise twice a week.

  1. Does this study make use of blocking? If so, what is the blocking variable?

ANSWER: It does, the blocking variable is age.

  1. Does this study make use of blinding?

ANSWER: No, both the researcher and participant knows what they were assigned.

  1. Comment on whether the results of the study can be used to establish a causal relationship between exercise and mental health and indicate whether the conclusions can be generalized to the population at large.

ANSWER: The results can be used to establish a causal relationship as the experiment used a stratified random sample which battles the confounding variable of age and the randomized nature blocks other confounding variable. These results can be generalized to people from 18-55 as those are the ages that were studied. A study would have to be done on the other age groups to be generalized to the rest of the population. This could only be generalized to exercising twice a week though as nothing else was studied.

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

ANSWER: Yes, I would like to know why they chose people to exercise only twice a week. I also feel that it is a bit unethical to force people to not exercise if you believe that this will cause peoples mental health to decrease because of it.

  1. Screens, teens, and psychological well-being. In a study of three nationally representative large-scale datasets from Ireland, the United States, and the United Kingdom (n = 17,247), teenagers between the ages of 12 to 15 were asked to keep a diary of their screen time and answer questions about how they felt or acted. The answers to these questions were then used to compute a psychological well-being score. Additional data were collected and included in the analysis, such as each childs sex and age, and on the mother’s education, ethnicity, psychological distress, and employment. The study concluded that there is little clear-cut evidence that screen time decreases adolescent well-being. (Orben and Baukney-Przybylski 2018)
  1. What type of study is this?

ANSWER: An observational study

  1. Identify the explanatory variables.

ANSWER: Screen time

  1. Identify the response variable.

ANSWER: Adolescent well-being

  1. Comment on whether the results of the study can be generalized to the population, and why.

ANSWER: It cannot as there was no control group and even though it states that these populations are nationally representative of these nations there is not quite enough information to prove that. There also seems to be no randomization.

  1. Comment on whether the results of the study can be used to establish causal relationships.

ANSWER: No, there is too many lurking variables in an observational study to establish causation

Date and time completed: Fri Sep 16 19:57:16 2022