# AP * Statistics Review. Designing a Study

 To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 video
Save this PDF as:

Size: px
Start display at page:

## Transcription

1 AP * Statistics Review Designing a Study Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production of, and does not endorse, this product.

2 Page 1 of 18 Population vs. Sample The population is the entire group you would like to study or draw a conclusion about. Any numerical value that comes from the population is a parameter. Parameters are usually unknown. The study of an entire population is called a census. The sample is the part of the population that you take data from. Any numerical value that comes from a sample is called a statistic. The goal of this course is to use statistics to draw conclusions or make statements about (unknown) parameters. You should recognize which symbols represent parameters from the entire population and which represent statistics from the sample: Parameter Statistic Mean μ x Standard deviation σ s x Proportion p pˆ Two kinds of studies In an observational study, people choose their own actions and scientists observe what they do. You cannot show a cause-and-effect relationship using an observational study. In an experiment, the scientist assigns treatments to subjects. A good experiment controls (or equalizes all the variables we are able to), randomizes the assignment of treatments to the subjects to hopefully equalize the variables we don t know about or cannot control, and replicates (uses a large sample size) to reduce variation. Bias Bias is when a study systematically favors one outcome over another. It can occur when a certain group is over- or under-represented in your sample or when your measurement device affects the results. (For example, survey questions could be worded to encourage a certain answer, or a scale could be calibrated wrong so that everything weighs too much.) Bias changes the center (mean or median) of your distribution. Bias may not be done on purpose, but it should be avoided. There is no mathematical way to fix biased data. Bad data leads to bad conclusions.

4 Page 3 of 18 Systematic random sample: choosing every 4 th name off a list or every 10 th person through a door. Vocabulary for experiments Example: You want to know what combination of fertilizer brand and watering frequency results in the most growth for a wheat plant. You are interested in 3 brands (A, B, and C) of fertilizer and you plan to water either twice a week or four times a week. Explanatory variable: x variable (called the independent variable in science class) Response variable: y variable (called the dependent variable in science class) Experimental units: What you are experimenting on (wheat plants) Factors: the explanatory variables (here, fertilizer brand and watering frequency) Levels: the choices you have for each factor (fertilizer brand has three levels and watering frequency has two levels) Treatments: the combinations you will test (there will be six treatments, which we find by multiplying the three levels for fertilizer by the two levels for watering) Completely Randomized Design (CRD): take the list of experimental subjects, number them, use the random number table to assign them to treatment groups, run the experiment for a given amount of time, then compare the groups on the response variable Considerations in Experimental Design A control group (which either gets no treatment or gets the old, established treatment) must be used for comparison. For example, if you are testing a treatment for a sprained ankle, you must have a group that gets no treatment because sprained ankles naturally get better over time. You need to show that the treatment group gets better faster than the control group. You want the treatment group and the control group to be as equal as possible, so that the only difference between the groups is the treatment itself. A placebo, or fake treatment, is used to equalize psychological effects between the groups. In a blind experiment, the subjects do not know if they are getting the treatment or the placebo. In a double blind experiment, the person handing out the treatments or the person evaluating the results also doesn t know which subjects are in which group. This is to equalize psychological effects. At the end of an experiment, if you can say that the difference between the groups could be due to variables A or B, then A and B are confounded variables. For example, suppose a group of boys was taught to read with Method 1 and a group of girls was taught with Method 2. If one group has higher reading scores, you cannot tell if it is due to the difference in gender or the difference in teaching method. Gender and teaching method are confounded.

5 Page 4 of 18 If your subjects have differences that could affect the response variable, you need to make sure the control group and the treatment group are as equal as possible by using blocking. For example, block design is necessary if you have 50 female and 20 male volunteers to use in a medication study, and you think that the medication might affect men and women differently. Form blocks by gender by putting the 50 females on one list and the 20 males on another. Randomly choose 25 females and 10 males to be in the treatment group. The remaining 25 females and 10 males will be the control group. Since both groups have the same gender makeup, any difference between the groups can be attributed to the medicine, not to gender differences. A matched pair design is a special case of block design in which each block consists of only 2 subjects. Match up the subjects so that they are as similar as possible, and then randomly choose one from each pair to be in the treatment group and the other to be in the control group.

6 Page 5 of 18 Multiple Choice Questions on Designing a Study 1. A human resources director of a large company is interested in how often employees use their computers during breaks. She watches a selected group of employees at their desks during the break times. This study would best be described as (A) a census (B) a survey (C) an observational study (D) an experiment (E) a sample 2. A company wants to compare two washing detergents (Brands A and B) to see which best keeps colors from fading. Twenty new, identical red t-shirts will be used in the trials. Ten t-shirts are washed 15 times with Brand A in warm water. The other 10 t-shirts are washed with Brand B in cold water. The amount of fading is rated on a 0 to 100 scale, and the mean for the t-shirts washed in Brand A is compared to the mean for the others. Is this a good experimental design? (A) No, because the means are not the proper statistics for comparison. (B) No, because more than two brands of detergent should be used. (C) No, because more temperatures of water should be used. (D) No, because water temperature is confounded with brand of detergent. (E) Yes. 3. The state would like to evaluate the usefulness of a program to randomly test high school athletes for steroid use. Initially, a state agency will test athletes in all 20 schools in Fort Worth, randomly selecting 3 athletes from each school. Is this a simple random sample of student athletes in Fort Worth? (A) Yes, because athletes will be chosen at random. (B) Yes, because each athlete is equally likely to be chosen. (C) Yes, because stratified sampling is a special case of simple random sampling (D) No, because not all possible groups of 60 athletes could be in the sample. (E) No, because a random sample of Ft. Worth schools is not chosen.

8 Page 7 of A student organization wants to assess the attitudes of students toward a proposed change in the hours the library is open. They randomly select 50 freshmen, 50 sophomores, 50 juniors, and 50 seniors to survey. This situation is described as (A) a stratified random sample (B) a simple random sample (C) a convenience sample (D) a systematic random sample (E) an observational study 8. A group of 420 college students are enrolled in a blind taste test. The school s food service wants to see if they can improve the taste of their lattes. They decide to try two types of coffee beans (Arabica and Robusta); three types of syrup (vanilla, hazelnut, and mocha); and two types of milk (soy and low fat). The best combination of ingredients is sought. The latte experiment will have (A) 2 factors, 7 levels, and 420 treatments (B) 2 factors, 3 levels, and 12 treatments (C) 3 factors, 7 levels, and 420 treatments (D) 3 factors, 12 levels, and 420 treatments (E) 3 factors, 7 levels, and 12 treatments 9. The primary reason for using blocking when designing an experiment is to reduce (A) variation (B) the need for randomization (C) bias (D) confounding (E) the sensitivity of the experiment

9 Page 8 of The head of the admissions office at a small college wants to understand why minority students who visit her school do not eventually enroll. The college holds a preview weekend for students who have been admitted. Two months later, after the students have decided while college to attend, a survey is sent out to all minority students who attended the weekend visit but who did not choose to attend this college. About a third of them returned the survey, with 48% of those indicating that they received a larger scholarship offer elsewhere. Which is true? I. The population of interest is all potential college students. II. This survey design suffered from non-response bias. III. Because it comes from a sample, 48% is a parameter, not a statistic. (A) (B) (C) (D) (E) I only II only I and II only II and III only I, II, and III

10 Page 9 of 18 Free Response Questions on Designing a Study 1. A veterinary school would like to test a food supplement that is meant to increase joint flexibility in dogs. Dogs lose flexibility as they age, with many older dogs (ages 8 and above) exhibiting joint problems. In addition, the joints of larger breeds of dogs are subject to more stress, so joint problems appear more frequently and more severely in larger dogs. Twelve dogs have been volunteered for this study by their owners. They have been categorized by age and size, where small breeds are under 35 pounds, medium breeds are 35 to 70 pounds, and large breeds are over 71 pounds. Owners will administer the food supplement to the six dogs chosen for the treatment group, while the other six dogs will be given a placebo by their owners. Before the study, the owners will complete a questionnaire about their dog s comfort and activity level. They will answer the same questions after three months of treatment, and the results will be compared. Dog Age Breed Size number 1 9 Large 2 6 Small 3 3 Large 4 5 Large 5 4 Small 6 6 Medium 7 5 Large 8 10 Medium 9 11 Large 10 2 Large 11 9 Medium 12 5 Medium a) A matched-pairs block design will be used for this study. Using the dog numbers, tell which dogs will be in each of the six blocks and describe the criteria used to form the blocks. b) Describe how the dogs will be assigned to the treatment or control group. c) Describe why a placebo is necessary in this study.

11 Page 10 of A new type of soy-based baby formula has been developed to help babies who have trouble gaining weight in their first six months of life. The parents of 150 babies have volunteered their children to participate in this study. All of the babies are between 8 and 9 weeks of age (a time when they should be growing very rapidly) and have been identified by their doctors as gaining weight more slowly than normal. The babies will be weighed before the study begins. Half of them will be given the new formula and the other half will be given the type of formula that is currently recommended for slowly growing babies. After three months, all the babies will be weighed again. a) Describe an appropriate method for assigning the subjects to the two groups so that each group will have an equal number of subjects. b) In this study, the researchers chose to include a group who used the currently recommended brand of formula. Why is it important to include a control group in this study even though weights will be measured at the beginning and at the end of the study? c) Many babies continue to drink formula until they are 12 to 15 months of age. Why would the researchers choose to use only babies who are about 2 months old (about 8 to 9 weeks old) in the study?

12 Page 11 of At a certain neighborhood public library, the librarian was interested in finding out if the users of the library would like more children s activities to be scheduled. Based on her conversations with parents, she believed that many library users put a high priority on children s activities. She decided to do a survey to estimate the proportion of adult library users who would like the number of children s activities to be increased. During month of July, the librarian asked the first twenty adults entering the library each morning to answer the following question: Many library users think that more children s activities should be provided at this library. Do you think that the number of children s activities should be increased, even though this would take away resources for other programs such as adult education or public internet access? Yes No No opinion (a) This survey used a convenience sample. In this situation, explain how bias may have been introduced based on the way this convenience sample was selected and suggest how the sample could have been selected differently to avoid that bias. (b) In this situation, explain how bias may have been introduced based on the way the question was worded and suggest how it could have been worded differently to avoid that bias.

13 Page 12 of 18 Key to Designing a Study Multiple Choice 1. C The workers themselves choose to use their computers or not, so this is an observational study. 2. D The difference in fading could be due to either detergent brand or water temperature, so this is an example of confounding. 3. D This is stratified, not simple. 4. C Distractors: A is undercoverage and non-response bias; B is undercoverage; D is voluntary response bias; E is response bias 5. D Use three digit numbers, and ignore numbers over D This is not a completely randomized design because the treatment group was not chosen randomly from a list of all 40 volunteers. Since the treatment group was chosen randomly from 2 separate lists (males and females), this study is blocked by gender. 7. A Since students are chosen from each group, this is a stratified random sample. 8. E Three factors (coffee, syrup, milk), 7 levels (2 choices of coffee, 3 choices of syrup, 2 choices of milk), and = 12 combinations 9. A Blocking groups together subjects that are similar and thus reduces variability that is attributable to the differences between the blocks. 10. B I is not true because the population of interest is minority students who have visited this college. II is true because only a third of the students returned the survey. III is false; 48% is a statistic because it comes from a sample.

14 Page 13 of 18 Rubric for Designing a Study Free Response 1. Solution Part (a): The blocks (by number) are 2 and 5 (small, younger) 6 and 12 (medium, younger) 8 and 11 (medium, older) 3 and 10 (large, quite young) 4 and 7 (large, young) 1 and 9 (large, older) Note: students must describe the blocks by number. They do not have to add the descriptions in parentheses. Dogs of similar size and age were assigned to the same block. Part (b): One dog from each block must be randomly assigned to the treatment group, and the other dog must go to the control group. A process must be described clearly enough that another person could carry it out. For example: a coin is tossed for each block. If it is heads, the lower-numbered dog goes to the treatment group and the higher-numbered dog goes to the control group. If it is tails, do the reverse. Or put the names of the two dogs in each block on slips of paper in a bag. Draw out one name. That dog goes to the treatment group and the other dog in the block goes to the control group. Repeat for each block. Part (c): Since the owners are the ones evaluating the results of the study, it is important that they not know if their dogs are getting the supplement or not. The use of a placebo allows the study to be blind. This prevents an owner from answering the questions differently or from changing other variables (such as the amount of exercise they give their dogs) that could affect the results of the study based on their knowledge of which group their dog is in. Scoring Parts (a) and (b) can be essentially correct (E), partially correct (P), or incorrect (I). Part (c) can be essentially correct (E) or incorrect (I). Part (a) is correct if the student correctly identifies the blocks and describes how blocks were assigned. Part (a) is partially correct if the student does one of the two tasks above. Part (a) is incorrect if the student does neither.

15 Page 14 of 18 Part (b) is correct if the method assigns one dog from each block to the control group and one to the treatment group and describes a clear method that results in a random assignment. Part (b) is partially correct if the process assigns one dog from each block to the treatment group but the process is not random, or a random process is used but it does not necessarily assign one dog from each block to the treatment group, or if the random process is not described clearly enough for someone else to follow it. Part (c) is correct if the student identifies the placebo as needed to make the study blind or to equalize psychological effects or knowledge in the owners. 4 Complete Response All parts essentially correct. 3 Substantial Response Two parts essentially correct and one part partially correct 2 Developing Response OR Two parts essentially correct and no parts partially correct One part essentially correct and two parts partially correct 1 Minimal Response One part essentially correct and either zero or one part partially correct OR No parts essentially correct and two parts partially correct

16 Page 15 of Solution Part (a): The student must clearly describe a random process that will choose 75 babies for the treatment group and 75 for the control group. For example, put the names of all of the volunteers on identical slips of paper, put them in a bag, shake them up, and pull out 75 slips. Those babies form the treatment group. The remaining 75 are the control group. OR Number a list of volunteers from 001 to 150. Look at three-digit numbers from a random number table. The first 75 non-repeated numbers between 001 and 150 will be the treatment group. The remaining volunteers will be the control group. OR Flip a coin for each participant. If it is heads, put that baby in the treatment group. Other wise, put the baby in the control group. Continue flipping coins until 75 babies have been chosen for the treatment group. The remaining babies will go in the control group. Part (b): All babies should gain some weight in a three month period beginning at the age of 8 to 9 weeks old. We must have a control group for comparison purposes so we can see if the treatment group gained more weight than the control group. Students may identify some other variable leading to weight gain (other than the natural weight gain as the babies get older), but they do not have to identify any other variable. Part (c): The babies chosen for the study are all about the same age in order to reduce variation. Babies of different ages are expected to grow at different rates, so choosing babies of the same approximate age helps insure that the groups are similar in growth rate, eliminating age as a confounding variable and allowing more direct comparison between the groups. Scoring Parts (a) and (b) can be essentially correct (E), partially correct (P), or incorrect (I). Part (c) can be essentially correct (E) or incorrect (I). Part (a) is essentially correct if the student describes a method that is based on random assignment and that will result in 75 babies in each group. Part (a) is partially correct if the student describes a random method that will not result in 75 babies in each group, or attempts to describe a method that will assign 75 babies to each group, but the explanation of random assignment is unclear or incomplete. Part (a) is incorrect if the method described is not random or if the student refers to random assignment without describing a method of assignment.

17 Page 16 of 18 Part (b) is essentially correct if the student states that the control group is needed for comparison purposes in order to see how much of the growth can be attributed to the new formula and how much would generally be expected with the old formula. Part (b) is partially correct if the student identifies that the control group is needed in order to compare the two groups but does not identify the need for comparison to control the other variables (such as the natural growth of the babies or another variable they have identified). Part (b) is incorrect if the student fails to see the need for a comparison group. Part (c) is correct if the student explains that age is related to growth and expresses the desire for more homogeneous groups or says that choosing babies of the same age will reduce variability. Part (c) is incorrect if the student only says that age is associated with growth or that age is a confounding variable. 4 Complete Response All parts essentially correct. 3 Substantial Response Two parts essentially correct and one part partially correct 2 Developing Response OR Two parts essentially correct and no parts partially correct One part essentially correct and two parts partially correct 1 Minimal Response One part essentially correct and either zero or one part partially correct OR No parts essentially correct and two parts partially correct

18 Page 17 of Solution Part (a): Bias may have been introduced by this convenience sample because the first people entering the library in the morning during the summer may differ in their opinions from those who use the library in the evenings or at other times. For example, many people going to the library during normal business hours during the summer may be parents with children who are out of school for summer break. These people would be more likely to support an increase in children s activities. Instead of gathering data using a convenience sample, surveys should be sent to a simple random sample of adults holding library cards at this branch or a simple random sample of adults who have used this library at any time during the past year. Part (b): The wording of the question may be leading. Since the question says that other people support an increase in children s activities, respondents may be more likely to agree with the statement. Since the question states that increasing children s activities may take resources away from other programs, some people may NOT support the increase in children s activities in order to maintain support of other programs they value. A better way to word the question would be to simply ask, Should the number of children s activities at this library be increased? Scoring Each part can be essentially correct (E), partially correct (P), or incorrect (I). Part (a) is essentially correct if the student indicates that choosing the first 20 people entering the library each July morning could introduce bias because those people s opinions might differ from those of other library users, and a random sample should be taken of library users (either an SRS or a systematic sample with a random starting point) Part (a) is partially correct if the student correctly does one of the above. Part (a) is incorrect if the student does neither. Part (b) is essentially correct if the student points out at least one of the wording problems with the survey, and addresses that concern raised with a reasonable alternative wording. Note: the student did not need to point out both wording problems. However, if they pointed out both problems, their alternative wording must correct both problems.

19 Page 18 of 18 Part (b) is partially correct if the student identifies one or both of the wording problems, but does not propose a reasonable alternative to fix the question. Part (b) is incorrect if the student points out both problems, but argues that one will increase the proportion in favor and one will decrease the proportion in favor, so that the two effects cancel each other out. 4 Complete Response Both parts essentially correct. 3 Substantial Response One part essentially correct and one part partially correct 2 Developing Response OR One part essentially correct and one part incorrect Both parts partially correct 1 Minimal Response One part partially correct

### Problems for Chapter 9: Producing data: Experiments. STAT 145-023. Fall 2015.

How Data are Obtained The distinction between observational study and experiment is important in statistics. Observational Study Experiment Observes individuals and measures variables of interest but does

### SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

Ch. 1 Introduction to Statistics 1.1 An Overview of Statistics 1 Distinguish Between a Population and a Sample Identify the population and the sample. survey of 1353 American households found that 18%

### Second Midterm Exam (MATH1070 Spring 2012)

Second Midterm Exam (MATH1070 Spring 2012) Instructions: This is a one hour exam. You can use a notecard. Calculators are allowed, but other electronics are prohibited. 1. [60pts] Multiple Choice Problems

### AP * Statistics Review. Descriptive Statistics

AP * Statistics Review Descriptive Statistics Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production

### c. Construct a boxplot for the data. Write a one sentence interpretation of your graph.

MBA/MIB 5315 Sample Test Problems Page 1 of 1 1. An English survey of 3000 medical records showed that smokers are more inclined to get depressed than non-smokers. Does this imply that smoking causes depression?

### AP Stats- Mrs. Daniel Chapter 4 MC Practice

AP Stats- Mrs. Daniel Chapter 4 MC Practice Name: 1. Archaeologists plan to examine a sample of 2-meter-square plots near an ancient Greek city for artifacts visible in the ground. They choose separate

### Chapter 6. Examples (details given in class) Who is Measured: Units, Subjects, Participants. Research Studies to Detect Relationships

Announcements: Midterm Friday. Bring calculator and one sheet of notes. Can t use the calculator on your cell phone. Assigned seats, random ID check. Review Wed. Review sheet posted on website. Fri discussion

### AP Statistics Chapters 11-13 Practice Test MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Statistics Chapters 11-13 Practice Test Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A company sponsoring a new Internet search engine

### STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8: CHAPTERS 7 TO 10, SAMPLE MULTIPLE CHOICE QUESTIONS 1. If two events (both with probability greater than 0) are mutually exclusive, then: A. They also must be independent. B. They also could

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) The government of a town needs to determine if the city's residents will support the

### STATISTICS 8, FINAL EXAM. Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4

STATISTICS 8, FINAL EXAM NAME: KEY Seat Number: Last six digits of Student ID#: Circle your Discussion Section: 1 2 3 4 Make sure you have 8 pages. You will be provided with a table as well, as a separate

### Use the following to answer questions 1 and 2:

Ch. 5 Review (Part I) Use the following to answer questions 1 and 2: IB Math Analysis A television station is interested in predicting whether voters in its viewing area are in favor of federal funding

### Self-Check and Review Chapter 1 Sections 1.1-1.2

Self-Check and Review Chapter 1 Sections 1.1-1.2 Practice True/False 1. The entire collection of individuals or objects about which information is desired is called a sample. 2. A study is an observational

### 1.1 What is statistics? Data Collection. Important Definitions. What is data? Descriptive Statistics. Inferential Statistics

1.1 What is statistics? Data Collection Chapter 1 A science (bet you thought it was a math) of Collecting of data (Chap. 1) Organizing data (Chap. 2) Summarizing data (Chap. 2, 3) Analyzing data (Chap.

### Determine whether the data are qualitative or quantitative. 8) the colors of automobiles on a used car lot Answer: qualitative

Name Score: Math 227 Review Exam 1 Chapter 2& Fall 2011 ********************************************************************************************************************** SHORT ANSWER. Show work on

### AP Statistics Chapter 1 Test - Multiple Choice

AP Statistics Chapter 1 Test - Multiple Choice Name: 1. The following bar graph gives the percent of owners of three brands of trucks who are satisfied with their truck. From this graph, we may conclude

### MATH 103/GRACEY PRACTICE QUIZ/CHAPTER 1. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

MATH 103/GRACEY PRACTICE QUIZ/CHAPTER 1 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use common sense to determine whether the given event

### Data Analysis, Statistics, and Probability

Chapter 6 Data Analysis, Statistics, and Probability Content Strand Description Questions in this content strand assessed students skills in collecting, organizing, reading, representing, and interpreting

### Selecting Research Participants

C H A P T E R 6 Selecting Research Participants OBJECTIVES After studying this chapter, students should be able to Define the term sampling frame Describe the difference between random sampling and random

### AP Statistics 2011 Scoring Guidelines

AP Statistics 2011 Scoring Guidelines The College Board The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in

### AP Stats - Probability Review

AP Stats - Probability Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. I toss a penny and observe whether it lands heads up or tails up. Suppose

### Best Practices for Helping All Students Get Ready for the SAT. Prepared for Idaho SDE January 2014

Best Practices for Helping All Students Get Ready for the SAT Prepared for Idaho SDE January 2014 SAT Readiness Program Agenda: SAT Introduction SAT Preparation The Official SAT Online Course PSAT Participation

### Choose a simple random sample of size three from the following employees of a small company.

Name: Date: 1. In order to select a sample of undergraduate students in the United States, I select a simple random sample of four states. From each of these states, I select a simple random sample of

### Lecture 13. Understanding Probability and Long-Term Expectations

Lecture 13 Understanding Probability and Long-Term Expectations Thinking Challenge What s the probability of getting a head on the toss of a single fair coin? Use a scale from 0 (no way) to 1 (sure thing).

### Review #2. Statistics

Review #2 Statistics Find the mean of the given probability distribution. 1) x P(x) 0 0.19 1 0.37 2 0.16 3 0.26 4 0.02 A) 1.64 B) 1.45 C) 1.55 D) 1.74 2) The number of golf balls ordered by customers of

### Math and Science Bridge Program. Session 1 WHAT IS STATISTICS? 2/22/13. Research Paperwork. Agenda. Professional Development Website

Math and Science Bridge Program Year 1: Statistics and Probability Dr. Tamara Pearson Assistant Professor of Mathematics Research Paperwork Informed Consent Pre-Survey After you complete the survey please

### 1. Answers will vary. Students might focus on the unsanitary or disgusting nature of. Teacher Notes for Investigation #1: Did You Wash Your Hands?

Teacher Notes for Investigation #1: Did You Wash Your Hands? This investigation builds on the two hand-washing studies that were discussed in the Introduction. The questions posed here are designed to

### GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER

GRADE 6 MATH: GROCERY SHOPPING AND THE QUILT OF A MATH TEACHER UNIT OVERVIEW This unit contains a curriculum- embedded Common Core aligned task and instructional supports. The task is embedded in a 2 3

### ADVICE FOR THE COLLEGE BOUND WATER POLO PLAYER by Dante Dettamanti Water Polo Coach Stanford University, 1977-2001

ADVICE FOR THE COLLEGE BOUND WATER POLO PLAYER by Dante Dettamanti Water Polo Coach Stanford University, 1977-2001 CHOOSING A COLLEGE IS ONE OF THE IMPORTANT DECISIONS THAT A STUDEN-ATHLETE WILL EVER MAKE.

### AP Statistics 2001 Solutions and Scoring Guidelines

AP Statistics 2001 Solutions and Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use

### AP Statistics Chapters 11-12 Practice Problems MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

AP Statistics Chapters 11-12 Practice Problems Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) Criticize the following simulation: A student

### MAT 155. Chapter 1 Introduction to Statistics. Key Concept. Basics of Collecting Data. 155S1.5_3 Collecting Sample Data.

MAT 155 Dr. Claude Moore Cape Fear Community College Chapter 1 Introduction to Statistics 1 1 Review and Preview 1 2 Statistical Thinking 1 3 Types of Data 1 4 Critical Thinking 1 5 Collecting Sample Data

### AP * Statistics Review. Probability

AP * Statistics Review Probability Teacher Packet Advanced Placement and AP are registered trademark of the College Entrance Examination Board. The College Board was not involved in the production of,

### Review for Grade 9 June Exam - Unit 9 - Probability and Statistics

Name: Date: Review for Grade 9 June Exam - Unit 9 - Probability and Statistics Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The last three days Alexa

### Performance Assessment Task Baseball Players Grade 6. Common Core State Standards Math - Content Standards

Performance Assessment Task Baseball Players Grade 6 The task challenges a student to demonstrate understanding of the measures of center the mean, median and range. A student must be able to use the measures

### Statistics 2014 Scoring Guidelines

AP Statistics 2014 Scoring Guidelines College Board, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks of the College Board. AP Central is the official online home

### AP Statistics Ch 4 Aim 9: Experimental Design: Multiple-Choice Questions

Page 1 of7 The following questions are from Barron's How to Prepare for the AP Statistics - 3 rd Edition. review book is extremely helpful and its purchase is strongly recommended. This There is a penalty

### Mathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight

Mathematics Assessment Collaborative Tool Kits for Teachers Looking and Learning from Student Work 2009 Grade Eight Contents by Grade Level: Overview of Exam Grade Level Results Cut Score and Grade History

### Practice Questions Answers for Second Exam 2012

Practice Questions Answers for Second Exam 2012 Formulas for the test This is NOT the formula sheet that will be provided on the exam. The parts in bold will NOT appear on the exam. Mean = np Standard

### Americans Not Taking Advantage of New Smart Phone Capabilities Younger adults and men are most comfortable with new functions

Press Contact: Corporate Communications Harris Interactive 212-539-9600 press@harrisinteractive.com Americans Not Taking Advantage of New Smart Phone Capabilities Younger adults and men are most with new

### Paper PO06. Randomization in Clinical Trial Studies

Paper PO06 Randomization in Clinical Trial Studies David Shen, WCI, Inc. Zaizai Lu, AstraZeneca Pharmaceuticals ABSTRACT Randomization is of central importance in clinical trials. It prevents selection

### SOCIETY OF ACTUARIES THE AMERICAN ACADEMY OF ACTUARIES RETIREMENT PLAN PREFERENCES SURVEY REPORT OF FINDINGS. January 2004

SOCIETY OF ACTUARIES THE AMERICAN ACADEMY OF ACTUARIES RETIREMENT PLAN PREFERENCES SURVEY REPORT OF FINDINGS January 2004 Mathew Greenwald & Associates, Inc. TABLE OF CONTENTS INTRODUCTION... 1 SETTING

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Ch. 4 Discrete Probability Distributions 4.1 Probability Distributions 1 Decide if a Random Variable is Discrete or Continuous 1) State whether the variable is discrete or continuous. The number of cups

### Statistics 151 Practice Midterm 1 Mike Kowalski

Statistics 151 Practice Midterm 1 Mike Kowalski Statistics 151 Practice Midterm 1 Multiple Choice (50 minutes) Instructions: 1. This is a closed book exam. 2. You may use the STAT 151 formula sheets and

### AP Psychology 2003 Scoring Guidelines

AP Psychology 2003 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation; permission for any other use must be sought from the Advanced

### Descriptive Statistics and Measurement Scales

Descriptive Statistics 1 Descriptive Statistics and Measurement Scales Descriptive statistics are used to describe the basic features of the data in a study. They provide simple summaries about the sample

### DRAFT. New York State Testing Program Grade 7 Common Core Mathematics Test. Released Questions with Annotations

DRAFT New York State Testing Program Grade 7 Common Core Mathematics Test Released Questions with Annotations August 2014 Developed and published under contract with the New York State Education Department

### Quiz CHAPTER 16 NAME: UNDERSTANDING PROBABILITY AND LONG- TERM EXPECTATIONS

Quiz CHAPTER 16 NAME: UNDERSTANDING PROBABILITY AND LONG- TERM EXPECTATIONS 1. Give two examples of ways that we speak about probability in our every day lives. NY REASONABLE ANSWER OK. EXAMPLES: 1) WHAT

### Chapter 7 Probability. Example of a random circumstance. Random Circumstance. What does probability mean?? Goals in this chapter

Homework (due Wed, Oct 27) Chapter 7: #17, 27, 28 Announcements: Midterm exams keys on web. (For a few hours the answer to MC#1 was incorrect on Version A.) No grade disputes now. Will have a chance to

### Technical/trade school, two-year, or four-year college? Public (state) or private college? Liberal arts or technical college?

Grade 11 Keep Rising What Does My Ideal College Look Like? By now, you may be certain that you want to attend college. But how do you learn more about different colleges? There are many factors to consider

### What is a P-value? Ronald A. Thisted, PhD Departments of Statistics and Health Studies The University of Chicago

What is a P-value? Ronald A. Thisted, PhD Departments of Statistics and Health Studies The University of Chicago 8 June 1998, Corrections 14 February 2010 Abstract Results favoring one treatment over another

### 6.042/18.062J Mathematics for Computer Science. Expected Value I

6.42/8.62J Mathematics for Computer Science Srini Devadas and Eric Lehman May 3, 25 Lecture otes Expected Value I The expectation or expected value of a random variable is a single number that tells you

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. A) ±1.88 B) ±1.645 C) ±1.96 D) ±2.

Ch. 6 Confidence Intervals 6.1 Confidence Intervals for the Mean (Large Samples) 1 Find a Critical Value 1) Find the critical value zc that corresponds to a 94% confidence level. A) ±1.88 B) ±1.645 C)

### Statistics Notes Revision in Maths Week

Statistics Notes Revision in Maths Week 1 Section - Producing Data 1.1 Introduction Statistics is the science that studies the collection and interpretation of numerical data. Statistics divides the study

### The Math. P (x) = 5! = 1 2 3 4 5 = 120.

The Math Suppose there are n experiments, and the probability that someone gets the right answer on any given experiment is p. So in the first example above, n = 5 and p = 0.2. Let X be the number of correct

### Value-Added Measures of Educator Performance: Clearing Away the Smoke and Mirrors

Value-Added Measures of Educator Performance: Clearing Away the Smoke and Mirrors (Book forthcoming, Harvard Educ. Press, February, 2011) Douglas N. Harris Associate Professor of Educational Policy and

### Elementary Statistics

Elementary Statistics Chapter 1 Dr. Ghamsary Page 1 Elementary Statistics M. Ghamsary, Ph.D. Chap 01 1 Elementary Statistics Chapter 1 Dr. Ghamsary Page 2 Statistics: Statistics is the science of collecting,

### Few things are more feared than statistical analysis.

DATA ANALYSIS AND THE PRINCIPALSHIP Data-driven decision making is a hallmark of good instructional leadership. Principals and teachers can learn to maneuver through the statistcal data to help create

### CITY OF MILWAUKEE POLICE SATISFACTION SURVEY

RESEARCH BRIEF Joseph Cera, PhD Survey Center Director UW-Milwaukee Atiera Coleman, MA Project Assistant UW-Milwaukee CITY OF MILWAUKEE POLICE SATISFACTION SURVEY At the request of and in cooperation with

### Hypothesis Tests for 1 sample Proportions

Hypothesis Tests for 1 sample Proportions 1. Hypotheses. Write the null and alternative hypotheses you would use to test each of the following situations. a) A governor is concerned about his "negatives"

### Statistics Class Level Test Mu Alpha Theta State 2008

Statistics Class Level Test Mu Alpha Theta State 2008 1. Which of the following are true statements? I. The histogram of a binomial distribution with p = 0.5 is always symmetric no matter what n, the number

### AP Statistics 2002 Scoring Guidelines

AP Statistics 2002 Scoring Guidelines The materials included in these files are intended for use by AP teachers for course and exam preparation in the classroom; permission for any other use must be sought

### Designing a Sampling Method for a Survey of Iowa High School Seniors

Designing a Sampling Method for a Survey of Iowa High School Seniors Kyle A. Hewitt and Michael D. Larsen, Iowa State University Department of Statistics, Snedecor Hall, Ames, Iowa 50011-1210, larsen@iastate.edu

### Gender Differences in Computer Technology Achievement

Gender Differences in Computer Technology Achievement Kimberly V. Hale Abstract This study examined gender differences in computer technology achievement. The setting was a central Georgia middle school.

### Hypothesis Testing. Steps for a hypothesis test:

Hypothesis Testing Steps for a hypothesis test: 1. State the claim H 0 and the alternative, H a 2. Choose a significance level or use the given one. 3. Draw the sampling distribution based on the assumption

### Problems Before Experimental Design Assessment #1 Answers

Problems Before Experimental Design Assessment #1 Answers 1. Below is a list of cities. Assign numbers to each city from left to right starting at 01. Use the line of random digits shown below to choose

### Mind on Statistics. Chapter 8

Mind on Statistics Chapter 8 Sections 8.1-8.2 Questions 1 to 4: For each situation, decide if the random variable described is a discrete random variable or a continuous random variable. 1. Random variable

### Observational Studies and Experiments. Statistics 50, Spring 2009

Observational Studies and Experiments Statistics 50, Spring 2009 Introduction Study purpose is often to investigate the relationship between two variables Do taller people make more money? Do magnets help

### GRADUATE SCHOOL. Should I go? When to go? Where? Tests Applying SMITH COLLEGE CAREER DEVELOPMENT OFFICE

SMITH COLLEGE CAREER DEVELOPMENT OFFICE GRADUATE SCHOOL Should I go? When to go? Where? Tests Applying NORTHAMPTON, MA 413-585-2582 F:413-585-2596 WWW.SMITH.EDU/CDO SHOULD I GO? There are two good reasons

### Cell Phone Impairment?

Cell Phone Impairment? Overview of Lesson This lesson is based upon data collected by researchers at the University of Utah (Strayer and Johnston, 2001). The researchers asked student volunteers (subjects)

### Elementary Statistics and Inference. Elementary Statistics and Inference. 17 Expected Value and Standard Error. 22S:025 or 7P:025.

Elementary Statistics and Inference S:05 or 7P:05 Lecture Elementary Statistics and Inference S:05 or 7P:05 Chapter 7 A. The Expected Value In a chance process (probability experiment) the outcomes of

### 13.0 Central Limit Theorem

13.0 Central Limit Theorem Discuss Midterm/Answer Questions Box Models Expected Value and Standard Error Central Limit Theorem 1 13.1 Box Models A Box Model describes a process in terms of making repeated

### Data Collection and Sampling OPRE 6301

Data Collection and Sampling OPRE 6301 Recall... Statistics is a tool for converting data into information: Statistics Data Information But where then does data come from? How is it gathered? How do we

### Online Senior Assessment 2013: Social and Behavioral Sciences

INTRODUCTION The sixth component of the OSA contains questions for the Social and Behavioral Sciences core. The first questions ask the participants about how they fulfilled their Social and Behavioral

### Research Design Concepts. Independent and dependent variables Data types Sampling Validity and reliability

Research Design Concepts Independent and dependent variables Data types Sampling Validity and reliability Research Design Action plan for carrying out research How the research will be conducted to investigate

### PROBABILITY. Thabisa Tikolo STATISTICS SOUTH AFRICA

PROBABILITY Thabisa Tikolo STATISTICS SOUTH AFRICA Probability is a topic that some educators tend to struggle with and thus avoid teaching it to learners. This is an indication that teachers are not yet

### Financial Education in schools: the experience of the Bank of Italy and the Ministry of Education

Financial Education in schools: the experience of the Bank of Italy and the Ministry of Education Maurizio Trifilidis Bank of Italy Background The individuals decision-making process could be improved

### 6.1. Construct and Interpret Binomial Distributions. p Study probability distributions. Goal VOCABULARY. Your Notes.

6.1 Georgia Performance Standard(s) MM3D1 Your Notes Construct and Interpret Binomial Distributions Goal p Study probability distributions. VOCABULARY Random variable Discrete random variable Continuous

### Inclusion and Exclusion Criteria

Inclusion and Exclusion Criteria Inclusion criteria = attributes of subjects that are essential for their selection to participate. Inclusion criteria function remove the influence of specific confounding

### AP Psychology 2000 Scoring Guidelines

AP Psychology 2000 Scoring Guidelines The materials included in these files are intended for non-commercial use by AP teachers for course and exam preparation; permission for any other use must be sought

### Standard 12: The student will explain and evaluate the financial impact and consequences of gambling.

STUDENT MODULE 12.1 GAMBLING PAGE 1 Standard 12: The student will explain and evaluate the financial impact and consequences of gambling. Risky Business Simone, Paula, and Randy meet in the library every

### Sample Exam #1 Elementary Statistics

Sample Exam #1 Elementary Statistics Instructions. No books, notes, or calculators are allowed. 1. Some variables that were recorded while studying diets of sharks are given below. Which of the variables

### Basic concepts in probability. Sue Gordon

Mathematics Learning Centre Basic concepts in probability Sue Gordon c 2005 University of Sydney Mathematics Learning Centre, University of Sydney 1 1 Set Notation You may omit this section if you are

### MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Final Exam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A researcher for an airline interviews all of the passengers on five randomly

### Introduction to Analysis of Variance (ANOVA) Limitations of the t-test

Introduction to Analysis of Variance (ANOVA) The Structural Model, The Summary Table, and the One- Way ANOVA Limitations of the t-test Although the t-test is commonly used, it has limitations Can only

### Statistical Fallacies: Lying to Ourselves and Others

Statistical Fallacies: Lying to Ourselves and Others "There are three kinds of lies: lies, damned lies, and statistics. Benjamin Disraeli +/- Benjamin Disraeli Introduction Statistics, assuming they ve

### Chapter 1: The Nature of Probability and Statistics

Chapter 1: The Nature of Probability and Statistics Learning Objectives Upon successful completion of Chapter 1, you will have applicable knowledge of the following concepts: Statistics: An Overview and

### The College Application Process Frequently Asked Questions Class of 2016

The College Application Process Frequently Asked Questions Class of 2016 What is our school code? Our CEEB Code is 390-488 How many students are in the class of 2016? There are approximately 565 students

### Fractions Packet. Contents

Fractions Packet Contents Intro to Fractions.. page Reducing Fractions.. page Ordering Fractions page Multiplication and Division of Fractions page Addition and Subtraction of Fractions.. page Answer Keys..

### Adults and Cell Phone Distractions

Adults and Cell Phone Distractions Mary Madden, Senior Research Specialist Lee Rainie, Director June 18, 2010 http://pewinternet.org/reports/2010/cell-phone-distractions.aspx Pew Internet & American Life

### ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers

ACMS 10140 Section 02 Elements of Statistics October 28, 2010 Midterm Examination II Answers Name DO NOT remove this answer page. DO turn in the entire exam. Make sure that you have all ten (10) pages

### 1 J (Gr 6): Summarize and describe distributions.

MAT.07.PT.4.TRVLT.A.299 Sample Item ID: MAT.07.PT.4.TRVLT.A.299 Title: Travel Time to Work (TRVLT) Grade: 07 Primary Claim: Claim 4: Modeling and Data Analysis Students can analyze complex, real-world

### Problem Solving and Data Analysis

Chapter 20 Problem Solving and Data Analysis The Problem Solving and Data Analysis section of the SAT Math Test assesses your ability to use your math understanding and skills to solve problems set in

### ESOL Customer Service Training: Unit 1 1: 1 Student Book. Unit 1: Talking With Your Customer

ESOL Customer Service Training: Unit 1 1: 1 Unit 1: Talking With Your Customer ESOL Customer Service Training: Unit 1 1: 2 What are your goals? Note to Instructor: If you have permission, use Stand Out

### STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS

STATISTICS 8 CHAPTERS 1 TO 6, SAMPLE MULTIPLE CHOICE QUESTIONS Correct answers are in bold italics.. This scenario applies to Questions 1 and 2: A study was done to compare the lung capacity of coal miners

1. Is the AP Exam the same across the nation? Yes, AP exam for the particular courses are the same across the nation. The test dates are the same for everyone. 2. How is the AP score calculated? See the

### PREPARING FOR LIFE AFTER HIGH SCHOOL

PREPARING FOR LIFE AFTER HIGH SCHOOL A College/Career Preparation Checklist Produced by the Winter Haven Academic Booster Club To complete online visit www.whhsabc.com WELCOME TO WINTER HAVEN! The Winter

### LONG-TERM CARE: The Associated Press-NORC Center for Public Affairs Research. Perceptions, Experiences, and Attitudes among Americans 40 or Older

The Associated Press-NORC Center for Public Affairs Research Research Highlights LONG-TERM CARE: Perceptions, Experiences, and Attitudes among Americans 40 or Older T. Tompson, J. Benz, J. Agiesta, D.