Dear Future AP Statistics Student, In order to ensure we have adequate time for all curriculum in Advanced Placement Statistics, the math department has designed a pre-assignment to help introduce the concepts of experimentation and research study. The assignment follows on pages 2 5 of this file. If you are receiving this in paper form or accessing this from the MND website, please email Ms. Schute (pschute@mndhs.org) for additional resources that were sent to students in May. The assignment will need to be submitted on the first AP Stats class at the beginning of second semester. Email any questions or concerns to the address below. Take care, Ms. Paula Schute Mathematics Department Chairperson pschute@mndhs.org 513.821.3044 711 E. Columbia Ave., Cincinnati, OH 45215 www.mndhs.org
The goal of this assignment is for you to become familiar with experiments and observational studies in the context of statistics. Use the resources on the assignment page (http://padlet.com/pschute/apstatspreassig) to learn about the concepts, process, and vocabulary of experiments and observational studies in statistics. Part 1: Create notecards for the terminology on the following page. These concepts are 10% - 15% of the exam content. Put definitions in your own words so you can use these to prepare for the AP test. Include diagrams and/or examples whenever appropriate. You should have the notecards to turn in the first day of class. Part 2: Access the file Preassignment Questions from the padlet page (http://padlet.com/pschute/apstatspreassig) and answer 2 of the 3 questions. You may type or ink your responses and the file should be submitted through Schoology on (or before) the first day of class. Terminology of Statistical Experiments & Observational Studies Population Parameter Sample Statistic Sample Survey Bias Census Representative sample Simple Random Sample (SRS) Sampling Frame Sampling Variability Stratified Sampling Cluster Sampling Systematic Sampling Multistage Sampling Voluntary Response Bias Convenience Sampling Undercoverage Nonresponse Bias Response Bias Observational Study Retrospective Study Prospective Study Experiment Cause-and-effect Levels Treatment Four principles of experimental design Statistically Significant Control Group Blinding Single-Blind Double-Blind Placebo Placebo Effect Randomized Block Design Matching Subjects (Matched Pairs) Confounding
1. Members of the research and development division of the bicycle tire manufacturer are investigating tread life of rubber bicycle tires. They have suggested that a study be conducted to determine whether bicycle tires produced using a new synthetic rubber compound have a longer tread life than the tread life of bicycle tires produced using the standard rubber compound. A researcher in the division suggested the study by designed in the following way. Select 60 identical bicycles and randomly assign 30 of those bicycles to one group, A, and the rest to a second group, B. all 60 bicycles will be equipped with front tires produced using the standard rubber compound. However, the bicycles in group A will be equipped with rear tires produced using the new synthetic rubber compound, while the bicycles in group B will be equipped with rear tires produced using the standard rubber compound. A total of 60 bicyclists will be randomly selected from the population of students at a local university who regularly ride a bicycle. The 60 bicycles will be randomly assigned to the 60 students (with different bicycle assigned to each student), and the students will be asked to ride the bicyles for a sixmonth period. At the end of the six-month period, the researcher will compare the mean amounts of rear tire tread wear for the bicyclists in the two groups. (a) What type of design had been proposed for the study? What is the response variable in the design? (b) Other than using a larger sample size, describe a better design for the study than the one proposed by the researcher. Explain why your design is better.
2. An environmental research agency conducted a study of a certain state s roadsides to estimate the mean number of discarded cans and bottles per mile of public road. The state s public roads were grouped into three types: Major highways: major paved roads designed for high traffic volume Minor highways: smaller paved roads designed for low traffic volume Unpaved roads: gravel and dirt roads There are about 100,000 miles of public roads in the state. The environmental research agency defined a sampling unit to be a one-mile segment of public road. Using a database supplied by the state s department of transportation, the agency randomly selected 30 one-mile road segments for each of the three types of roads. Researchers from the agency searched the roadsides along each of the selected one-mile road segments and recorded the number of discarded cans and bottles. Results are shown in the table below. (a) What is the variable of interest in the study? What is the parameter of interest? (b) Were the data in the study obtained by a simple random sample, a stratified random sample, or a cluster sample? Explain.
3. Researchers investigated the possible beneficial effect on heart health of drinking black tea and whether adding milk to the tea reduced any possible benefit. Twenty-four volunteers were randomly assigned to one of three groups. Every day for a month, participants in group 1 drank two cups of hot tea without milk, participants in group 2 drank two cups of hot black tea with milk, and participants in group 3 drank two cups of hot water but no tea. At the end of the month, the researchers measured the change in each of the participants heart health. (a) Did the researchers conduct and experiment or an observational study? Explain. (b) Why did the researchers include a group who drank hot water but no tea? (c) Is it reasonable to generalize the results of the study beyond the 24 participants? Explain why or why not.