Problem 3. [p-value and complete testing setup]
We would like to find out the following: Has the proportion of U.S. adults who support the death penalty for convicted murderers changed since 2003, when it was 0.64? We take a random sample of 1000 US adults and learn that 675 are in favor of the death penalty for convicted murderers.
- What is the population parameter we are testing?
- Set up the null and alternative hypothesis.
- State the test statistic (formula) and compute the observed value of the test statistic.
- Compute the p-value of this data.
- Draw your conclusion.
Setup for problems 4 & 5.
College students at a large state university completed a survey about their academic and personal life. Questions ranged from How many credits are you registered for this semester? to Would you define yourself as a vegetarian? Four sections of an introductory statistics course were chosen at random from all the sections of introductory statistics courses offered at the university in the semester when the survey was conducted, and the 312 students who completed the survey were students registered in one of the four chosen sections.
In this exercise, we will use a subset of variables from the survey and use the collected data to answer three questions. Note that (1) these are real data, and (2) the symbol * means that this observation is not available (this is known as a missing value).
Here are the variables in the data and their meaning:
- Math: Math SAT score
- Verbal: Verbal SAT score
- Credits: Number of credits the student is registered for
- Year: Year in college (1=Freshman, 2=Sophomore, 3=Junior, 4=Senior)
- Exer: Time (in minutes) spent exercising in a typical day
- Sleep: Time (in hours) spent sleeping in a typical day
- Veg: Are you a vegetarian (yes, no, some)
- Cell: Do you own a cell phone (yes, no)
Problem 4. [Understand the data]
We will start by answering some questions about the data.
- Out of the first ten students in the datafile, how many did better on the verbal portion of the SAT compared to the math portion?
- Out of the first ten students in the datafile, how many are at least somewhat vegetarian?
- How many hours does the first junior in the datafile who does not own a cell phone spend sleeping in a typical day?
- The next step in understanding the problem is addressing the issues of sampling and study design, which have implications on the generalizability of the results and the type of conclusions you can draw from them.
- Is this an observational study or an experiment?
- Briefly describe what the problem statement tells us about how the individuals in the dataset were selected to be in the sample.
Problem 5, option A. [You have 3 options to choose from; solve A or B.]
The mean verbal SAT score of all the students in this university is 580. Is this also the case for all stat students at this university? Note that verbal SAT scores in the U.S. have a standard deviation of 111.
- Identify which of the variables in the sample are relevant to each question.
- What population parameter are you exploring?
- What is the relevant statistic for this parameter?
- Which test will you use and why?
- Complete the computation.
Problem 5, option B. [You have 3 options to choose from; solve A or B.]
Based on a recent study, roughly 80% of college students in the U.S. own a cell phone. Do the data provide evidence that the proportion of students who own cell phones in this university is lower than the national figure?
- Identify which of the variables in the sample are relevant to each question.
- What population parameter are you exploring?
- What is the relevant statistic for this parameter?
- Which test will you use and why?
- Complete the computation.
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