Section 1: True or False

Instructions: For each of the following statements decide whether or not the statement is true or false. No justication is required, and no partial credit will be given.

  1. When two numerical variables are associated, one necessarily causes the other to increase.
  2. A cluster sampling strategy creates an unbiased sample when there is lots of variation within a cluster, but not much variation across different clusters.
  3. Students with many deltas often have very low GPAs. Thus, if we eliminated deltas everyone who has many deltas would see a rise in their GPA.
  4. A data matrix stores observations as rows and variables as columns.
  5. In a simple random sample, each observation from the population has an equal chance of being selected for the sample.

Section 2: Free response

Instructions: Carefully read each of the following questions and thoughtfully answer each part of the question using complete sentences and precise notation. Partial credit will be given for responses that clearly justify reasoning and outline procedures.

Question 1: Police killings

Recently, an report has been made by journalists to compile a dataset which tracks every person who was killed by a police officer. As of June 12, 2015, there were 13 people who were killed by police officers in the state of Colorado in 2015. The dataset collects data on those who were killed including names, race, age, gender, and whether or not they were armed.

  1. If you were to construct a data matrix from this data how many rows would it have? How many columns would it have?
  2. What are the observations in the data matrix?
  3. For this data matrix list each variable as well as its type and subtype.

Question 2: Car color data matrix

While sitting on the corner of Federal and Mississippi you record the color of the first 5 cars that drive by. You record the colors as {Red, Green, Black, Black, Black}.

  1. Place this data in a data matrix.

Question 3: Diabetes medication

Your friend’s dad has diabetes and took an experimental new drug designed to regulate the disease. Shortly after starting the medication he had a heart attack. Your friend concludes that the drug did not work and may in fact be dangerous. Explain why your friend’s conclusion about how effective the drug is might not be valid.

Question 4: Teacher experience and pay

The scatterplot below shows a teacher’s experience in years versus their salary in dollar.

  1. Does there seem to be an association between the number of years a teacher has been teaching and the amount of money the teacher makes? If so, is the association positive or negative?
  2. If there is an association can we necessarily assume the the number of years a teacher has been teaching causes a teacher’s pay to change?
  3. State one confounding variable that is associated with both years of teaching experience and teacher pay that might confound the causal relationship shown in the scatterplot.

Question 5: Advertising and sales

Vans Shoes begins an advertising campaign on December 1st. The advertising manager tracks shoe sales for each day of the month of December and notes that shoe sales steadily increase throughout the month. On December 20th the advertising manager declares that the sales campaign caused sales to sky rocket and was a overwhelming success. Explain why the sales manager’s claim may not be correct. What confounding variable may be a ecting the sales of shoes?

Question 6: Denver charter schools

You are interested in estimating the percent of all families in Denver who have school age childen and send those children to charter schools. You do not have time to take a census, so you decide to take a random sample of 300 families who have school age children and then calculate the percentage of these families that send their children to charter schools.

  1. What is the population of interest?
  2. What is the parameter of interest?
  3. What is the sample?
  4. What is the sample statistic?

Question 7: Sampling major league baseball salaries

Suppose you are interested in estimating the average salary of Major League Baseball players. Rather than waste your time looking up each player’s salary you decide to take a sample. Which sampling strategy discussed in class do you feel would do the best job of selecting a sample which fairly represents each team in the league?

Question 8: Percent of students applying to college at SMART

Suppose you want to estimate the percent of seniors at SMART who would like to apply for college. You don’t have time to survey every student at SMART so you decide to take a sample and then use the percent of students in the sample who would like to apply for college as your estimate of the population percentage.

  1. Give an example of a sampling strategy that would generate a simple random sample.
  2. Give an example of a strategy that would introduce bias into the sample.

Question 9: Sampling school satisfaction

You are in charge of administering a school satisfaction survey. Because you have limited time, you decide you will sample 100 students rather than the entire student population. You consider two sampling strategies. In the first strategy you will randomly select 25 students from each grade level to take the survey. In the second strategy you will choose 4 classes at random during a certain period of the day and have every student in each of these four classes take the survey.

  1. Give the names of the two sampling strategies described above.
  2. Which of these two strategies is most likely to give a sample which accuratel represents how students feel about school? Defend your reasoning.

Question 10: Experimental math

Mr. Garduno and Bradshaw are interested in testing the effectiveness of using a new online math curriculum. Rather than immediately using the curriculum they decide to design an experiment to test whether or not the curriculum works. They decide to have Mr. Garduno (21 years of teaching experience) use the curriculum in his classes, while Bradshaw (2 years teaching experience) will not use the curriculum in his classes. After 2 months, they find students in Mr. Garduno’s classes did much better on the IA exam and they conclude the curriculum is a success and they will implement it in all classes.

  1. Critique the experiment designed by Bradshaw and Mr. Garduno. Did they make a good decision in buying the curriculum based on this experiment?

Question 11: Designing an experiment

You are a cancer researcher and believe you have come up with a new cancer drug that may be effective in treating brain cancer. However, in order to be sure you need to design an experiment. You enlist 500 subjects with brain cancer.

  1. How would you design the experiment? Be sure to outline the methods you would use in designing and use diagrams if you feel it would be helpful in explaining and outlining your design.