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# Statistics Section 110 Math 1680

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This 28 page Class Notes was uploaded by Caroleen Bejimi on Thursday August 18, 2016. The Class Notes belongs to Math 1680 at University of North Texas taught by Lucia xiaoxing in Fall 2016. Since its upload, it has received 12 views. For similar materials see Statistics in Math at University of North Texas.

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Date Created: 08/18/16

Chapter 1 – Data Collection OUTLINE Putting It Together 1.1 Introduction to the Practice of StatisticsStatistics plays a major role in many aspects of 1.2 Observational Studies versus Designed our lives. It is used in sports, for example, to Experiments help a general manager decide which player 1.3 Simple Random Sampling might be the best fit for a team. It is used in 1.4 Other Effective Sampling Methods politics to help candidates understand how the public feels about various policies. And statistics 1.5 Bias in Sampling 1.6 The Design of Experiments is used in medicine to help determine the effectiveness of new drugs. Used appropriately, statistics can enhance our understanding of the world. Used inappropriately, it can lend support to inaccurate beliefs. Understanding statistical methods will provide you with the ability to analyze and critique studies and the opportunity to become an informed consumer of information. Understanding statistical methods will also enable you to distinguish solid analysis from bogus “facts.” Copyright © 2016 Pearson Education, Inc. 1 Chapter 1: Data Collection Section 1.1 Introduction to the Practice of Statistics Objectives ▯ Define statistics and statistical thinking ▯ Explain the process of statistics ▯ Distinguish between qualitative and quantitative variables ▯ Distinguish between discrete and continuous variables ❺ Determine the level of measurement of a variable Objective 1: Define Statistics and Statistical Thinking Answer the following as you watch the video. 1) Write the definition of statistics below. 2) Data describes _______________ of individuals and can be either _______ or ___________. Note: Data varies. Consider the students in your class. Is everyone the same height? No. Does everyone have the same color hair? No. So, within groups there is variation. Now consider yourself. Do you eat the same amount of food (as measured by calories) each day? No. Do you sleep the same number of hours each day? No. So, even considering individuals there is variation. One goal of statistics is to describe and understand sources of variation. Objective 2: Explain the Process of Statistics Answer the following while watching the animation. 3) What is the entire group to be studied called? 4) What do we call a person or object that is a member of the population being studied? Copyright © 2016 Pearson Education, Inc. 2 Section 1.1: Introduction to the Practice of Statistics 5) Give the definition of a sample. 6) What do we call a numerical summary of a sample? 7) What do we call a numerical summary of a population? 8) Give the definition of descriptive statistics. 9) Give the definition of inferential statistics. Answer these questions after watching the animation. 10) In the $100 experiment, what is the population? What is the sample? Population: Sample: Copyright © 2016 Pearson Education, Inc. 3 Chapter 1: Data Collection 11) Is the statement an example of descriptive statistics or inferential statistics? Circle the correct answer. A) The percent of students in the survey who would return the money to the owner is 78%. s c i t s i t a t s l a i t nsecr ie s Ii t a t s e v i t p i r c s eD B) We are 95% confident that between 74% and 82% of all students would return the money. s c i t s i t a t s l a i t nsecr ie s Ii t a t s e v i t p i r c s eD 12) Is the given measure a statistic or a parameter? Circle the correct answer. A) The percentage of all students on your campus who own a car is 48.2%. c i rtestiet a rSPa B) Suppose a random sample of 100 students is obtained, and from this sample we find that 46% own a car. Statistic Parameter Fill in the following steps. The Process of Statistics 1. A researcher must determine the question(s) he or she wants answered. The question(s) must be detailed so that it identifies the population that is to be studied. 2. Conducting research on an entire population is often difficult and expensive, so we typically look at a sample. This step is vital to the statistical process because if the data are not collected correctly, the conclusions drawn are meaningless. Do not overlook the importance of appropriate data collection. 3. Descriptive statistics allow the researcher to obtain an overview of the data and can help determine the type of statistical methods the researcher should use. 4. Apply the appropriate techniques to extend the results obtained from the sample to the population and report a level of reliability of the results. Copyright © 2016 Pearson Education, Inc. 4 Section 1.1: Introduction to the Practice of Statistics Example 1 The Process of Statistics: Gun Ownership The AP – National Constitution Center conducted a national poll to learn how adult Americans feel existing gun-control laws infringe on the second amendment to the U.S. Constitution. The following statistical process allowed the researchers to conduct their study. 1. Identify the research objective. 2. Collect the information needed to answer the question posed in (1). 3. Describe the data. 4. Perform inference. Objective 3: Distinguish between Qualitative and Quantitative Variables Define the following terms. 13) Qualitative variable: 14) Quantitative variable: Copyright © 2016 Pearson Education, Inc. 5 Chapter 1: Data Collection Example 2 Distinguishing between Qualitative and Quantitative Variables Determine whether the following variables are qualitative or quantitative. A) Gender B) Temperature C) Number of days during the past week that a college student studied D) Zip code Objective 4: Distinguish between Discrete and Continuous Variables Define the following terms. 15) Discrete variable: 16) Continuous variable: Copyright © 2016 Pearson Education, Inc. 6 Section 1.1: Introduction to the Practice of Statistics Example 3 Distinguishing between Discrete and Continuous Variables Determine whether the quantitative variables are discrete or continuous. A) The number of heads obtained after flipping a coin five times. B) The number of cars that arrive at a McDonald’s drive-through between 12:00 P.M. and 1:00 P.M. C) The distance a 2011 Toyota Prius can travel in city driving conditions with a full tank of gas. Define the following terms. 17) Data: 18) Qualitative data: 19) Quantitative data: 20) Discrete data: Copyright © 2016 Pearson Education, Inc. 7 Chapter 1: Data Collection 21) Continuous data: Example 4 Distinguishing between Variables and Data The following table presents a group of selected countries and information regarding these countries as of September, 2010. Country Government Type Life Expectancy Population (in (years) millions) Australia Federal parliamentary democracy 81.63 21.3 Canada Constitutional monarchy 81.23 33.5 France Republic 80.98 64.4 Morocco Constitutional monarchy 75.47 31.3 Poland Republic 75.63 38.5 Sri Lanka Republic 75.14 21.3 United States Federal republic 78.11 307.2 Identify the individuals, variables, and data. Objective 5: Determine the Level of Measurement of a Variable List the characteristics used to determine what level of measurement a variable is. 22) Nominal: 23) Ordinal: Copyright © 2016 Pearson Education, Inc. 8 Section 1.1: Introduction to the Practice of Statistics 24) Interval: 25) Ratio: Example 5 Determining the Level of Measurement of a Variable For each of the following variables, determine the level of measurement. A) Gender B) Temperature C) Number of days during the past week that a college student studied D) Letter grade earned in your statistics class Copyright © 2016 Pearson Education, Inc. 9 Chapter 1: Data Collection Section 1.2 Observational Studies versus Designed Experiments Objectives ▯ Distinguish between an observational study and a designed experiment ▯ Explain the various types of observational studies Objective 1: Distinguish between an Observational Study and a Designed Experiment Answer the following as you watch the video. 1) Why is the Danish study mentioned in the video an observational study and not a designed experiment? 2) Why is the “rat” study mentioned in the video a designed experiment and not an observational study? 3) What is the response variable in each study, and what is the explanatory variable? Answer the following after watching the first video in this objective. 4) In research, we wish to determine how varying an explanatory variable affects the value of what? 5) The response variable can be thought of as … Copyright © 2016 Pearson Education, Inc. 10 Section 1.2: Observational Studies versus Designed Experiments 6) What does an observational study measure? Does an observational study attempt to influence the value of the response variable or explanatory variable? 7) Explain how to determine if a study is a designed experiment. Watch the second video in this objective and answer the following. 8) Why is the influenza study mentioned in the video an observational study and not a designed experiment? 9) List some changes that could be made to investigate the effectiveness of the flu shot with a designed experiment. 10) List some lurking variables in the influenza study. Answer the following after watching the video. 11) Do observational studies allow a researcher to claim causality? Copyright © 2016 Pearson Education, Inc. 11 Chapter 1: Data Collection 12) Define confounding in a study. 13) What is a lurking variable? Define the following term. 14) Confounding variable: Note: The big difference between lurking variables and confounding variables is that lurking variables are not considered in the study whereas confounding variables are measured in the study. Objective 2: Explain the Various Types of Observational Studies Answer the following after watching the video. 15) List some of the advantages of performing a case-control study over a cross-sectional study. 16) List some difficulties that may occur and affect the outcomes of a case-control study. 17) Explain why the Cancer Prevention Study II conducted by the American Cancer Society is a cohort study. Copyright © 2016 Pearson Education, Inc. 12 Section 1.2: Observational Studies versus Designed Experiments Watch the video and answer the following. Define the following. 18) Cross-sectional studies 19) Case-control studies 20) Cohort studies 21) It is not always possible to conduct an experiment. Explain why we could not conduct an experiment to investigate the perceived link between high tension wires and leukemia (on humans). 22) There is no point in reinventing the wheel. List some agencies that regularly collect data that are available to the public. 23) What is a census? 24) Why is the U.S. Census so important? Copyright © 2016 Pearson Education, Inc. 13 Chapter 1: Data Collection Section 1.3 Simple Random Sampling Objective ▯ Obtain a simple random sample Note: Sampling Observational studies can be conducted by administering a survey. When administering a survey, the researcher must first identify the population that is to be targeted. 1) Define random sampling: For the results of a survey to be reliable, the characteristics of the individuals in the sample must be representative of the characteristics of the individuals in the population. The key to obtaining a sample representative of a population is to let chance or randomness play a role in dictating which individuals are in the sample, rather than convenience. If convenience is used to obtain a sample, the results of the survey are meaningless. Objective 1: Obtain a Simple Random Sample 2) What is a simple random sample? The number of individuals in the sample is always less than the number of individuals in the population. Example 1 Illustrating Simple Random Sampling Sophie has four tickets to a concert. Six of her friends, Yolanda, Michael, Kevin, Marissa, Annie, and Katie, have all expressed an interest in going to the concert. Sophie decides to randomly select three of her six friends to attend the concert. Copyright © 2016 Pearson Education, Inc. 14 Section 1.3: Simple Random Sampling A) List all possible samples of size n = 3 from the population of size N = 6. Once an individual is chosen, he/she cannot be chosen again. B) Comment on the likelihood of the sample containing Michael, Kevin, and Marissa. Note: How do we select the individuals in a simple random sample? Typically, each individual in the population is assigned a unique number between 1 and N, where N is the size of the population. Then n distinct random numbers are selected, where n is the size of the sample. To number the individuals in the population, we need a frame - a list of all the individuals within the population. Answer the following after watching the animation. 3) What is the frame in this animation? 4) Explain why a second sample of 5 students will most likely be different than the first sample of 5 students? 5) Explain why inferences based on samples vary. Copyright © 2016 Pearson Education, Inc. 15 Chapter 1: Data Collection Example 2 Obtaining a Simple Random Sample The accounting firm of Senese and Associates has grown. To make sure their clients are still satisfied with the services they are receiving, the company decides to send a survey out to a simple random sample of 5 of its 30 clients. Copyright © 2016 Pearson Education, Inc. 16 Section 1.4: Other Effective Sampling Methods Section 1.4 Other Effective Sampling Methods Objectives ▯ Obtain a stratified sample ▯ Obtain a systematic sample ▯ Obtain a cluster sample Objective 1: Obtain a Stratified Sample 1) Explain how to obtain a stratified sample. Example 1 Obtaining a Stratified Sample The president of DePaul University wants to conduct a survey to determine the community’s opinion regarding campus safety. The president divides the DePaul community into three groups: resident students, nonresident (commuting) students, and staff (including faculty) so that he can obtain a stratified sample. Suppose there are 6,204 resident students, 13,304 nonresident students, and 2,401 staff, for a total of 21,909 individuals in the population. What percent of the DePaul community is made up of each group? The president wants to obtain a sample of size 100, with the number of individuals selected from each stratum weighted by the population size. How many individuals should be selected from each stratum? To obtain the stratified sample, construct a simple random sample within each group. Copyright © 2016 Pearson Education, Inc. 17 Chapter 1: Data Collection Objective 2: Obtain a Systematic Sample 2) Explain how to obtain a systematic sample. Note: Because systematic sampling does not require a frame, it is a useful technique when you cannot gather a list of the individuals in the population. Example 2 Obtaining a Systematic Sample without a Frame The manager of Kroger Food Stores wants to measure the satisfaction of the store’s customers. Design a sampling technique that can be used to obtain a sample of 40 customers. Answer the following after watching the first video after Example 2. 3) What can result from choosing a value of k that is too small? 4) What can result from choosing a value of k that is too large? Answer the following after watching the second video after Example 2. 5) Explain how to determine the value of k if the population size N is known. 6) List the five steps in obtaining a systematic sample. Step 1 Copyright © 2016 Pearson Education, Inc. 18 Section 1.4: Other Effective Sampling Methods Step 2 Step 3 Step 4 Step 5 Objective 3: Obtain a Cluster Sample 7) What is a cluster sample? Example 3 Obtaining a Cluster Sample A sociologist wants to gather data regarding household income within the city of Boston. Obtain a sample using cluster sampling. Copyright © 2016 Pearson Education, Inc. 19 Chapter 1: Data Collection Read the screen “Issues to Consider in Cluster Sampling” and answer the following. 8) If the clusters have homogeneous individuals, is it better to have more clusters with fewer individuals in each cluster or fewer clusters with more individuals in each cluster? 9) If the clusters have heterogeneous individuals, is it better to have more clusters with fewer individuals in each cluster or fewer clusters with more individuals in each cluster? 10) Define convenience sampling: Note: The most popular convenience samples are those in which the individuals in the sample are self- selected, meaning the individuals themselves decide to participate in thesurvey. Self-selected surveys are also called voluntary response samples. 11) List an example of a scenario involving multistage sampling. Note: Sample Size Considerations Researchers need to know how many individuals they must survey to draw conclusions about the population within some predetermined margin of error. They must find a balance between the reliability of the results and the cost of obtaining these results. The bottom line is that time and money determine the level of confidence researchers will place on the conclusions drawn from the sample data. The more time and money researchers have available, the more accurate the results of the statistical inference. Copyright © 2016 Pearson Education, Inc. 20 Section 1.5: Bias in Sampling Section 1.5 Bias in Sampling Objective ▯ Explain the sources of bias in sampling Objective 1: Explain the Sources of Bias in Sampling 1) Define bias. 2) List the three sources of bias in sampling: • • • Answer the following after watching the video “Sampling Bias.” 3) What is sampling bias? 4) Does a convenience sample have sampling bias? Copyright © 2016 Pearson Education, Inc. 21 Chapter 1: Data Collection 5) What is undercoverage? Answer the following after watching the video “Nonresponse Bias.” 6) When does nonresponse bias exist? 7) List two causes of nonresponse bias. 8) List one tool that can be used to control nonresponse bias? Answer the following after watching the video “Response Bias.” 9) Under what conditions does response bias exist? Note: Response bias can occur through interviewer error, misrepresented answers, wording of questions, ordering of questions or words, type of question, or data-entry error. Note: An open question allows the respondent to choose his or her response (free response). Copyright © 2016 Pearson Education, Inc. 22 Section 1.5: Bias in Sampling Note: A closed question requires the respondent to choose from a list of predetermined responses (multiple choice). Note: Can a Census Have Bias? A question on a census form could be misunderstood, thereby leading to response bias in the results. It is often difficult to contact each individual in a population. For example, the U.S. Census Bureau is challenged to count each homeless person in the country, so the census data published by the U.S. government likely suffers from nonresponse bias. Define the following terms. 10) Nonsampling Error: 11) Sampling error: Copyright © 2016 Pearson Education, Inc. 23 Chapter 1: Data Collection Section 1.6 The Design of Experiments Objectives ▯ Describe the characteristics of an experiment ▯ Explain the steps in designing an experiment ▯ Explain the completely randomized design ▯ Explain the matched-pairs design Objective 1: Describe the Characteristics of an Experiment Define the following terms after watching the video. 1) Experiment: 2) Factor: 3) Treatment: 4) Experimental unit: 5) Control group: Copyright © 2016 Pearson Education, Inc. 24 Section 1.6: The Design of Experiments 6) Placebo: 7) Blinding: 8) Single-blind 9) Double-blind Example 1 The Characteristics of an Experiment Lipitor is a cholesterol-lowering drug made by Pfizer. In the Collaborative Atorvastatin Diabetes Study (CARDS), the effect of Lipitor on cardiovascular disease was assessed in 2838 subjects, ages 40 to 75, with type 2 diabetes, without prior history of cardiovascular disease. In this placebo-controlled, double- blind experiment, subjects were randomly allocated to either Lipitor 10 mg daily (1428) or placebo (1410) and were followed for 4 years. The response variable whether there was an occurrence of any major cardiovascular event or not. Lipitor significantly reduced the rate of major cardiovascular events (83 events in the Lipitor group versus 127 events in the placebo group). There were 61 deaths in the Lipitor group versus 82 deaths in the placebo group. A) What does it mean for the experiment to be placebo-controlled? B) What does it mean for the experiment to be double-blind? Copyright © 2016 Pearson Education, Inc. 25 Chapter 1: Data Collection C) What is the population for which this study applies? What is the sample? D) What are the treatments? E) What is the response variable? Is it qualitative or quantitative? Objective 2: Explain the Steps in Designing an Experiment Steps in Conducting a Designed Experiment Fill in each step. Step 1: ________________________________________________ The statement of the problem should be as explicit as possible and should provide the experimenter with direction. The statement must also identify the response variable and the population to be studied. Often, the statement is referred to as the claim. Step 2: ________________________________________________ The factors are usually identified by an expert in the field of study. In identifying the factors, ask, “What things affect the value of the response variable?” After the factors are identified, determine which factors to fix at some predetermined level, which to manipulate, and which to leave uncontrolled. Step 3: ________________________________________________ As a general rule, choose as many experimental units as time and money allow. Techniques exist for determining sample size, provided certain information is available. Copyright © 2016 Pearson Education, Inc. 26 Section 1.6: The Design of Experiments Step 4: ________________________________________________ Factors can be dealt with in two ways - control or randomize. Control means to either set the factor at one value throughout the eriment or set the level of the factor at various levels). Randomize means to randomly assign the experimental units to various treatment groups. Step 5: ________________________________________________ Replication occurs when each treatment is applied to more than one experimental unit. Step 6: ________________________________________________ Inferential statistics is a process in which generalizations about a population are made on the basis of results obtained from a sample. Objective 3: Explain the Completely Randomized Design 10) What is a completely randomized design? Example 2 A Completely Randomized Design A farmer wishes to determine the optimal level of a new fertilizer on his soybean crop. Design an experiment that will assist him. Copyright © 2016 Pearson Education, Inc. 27 Chapter 1: Data Collection Objective 4: Explain the Matched-Pairs Design 11) What is a matched-pairs design? The pairs are selected so that they are related in some way. There are only two levels of treatment in a matched-pairs design. Example 3 A Matched-Pairs Design An educational psychologist wants to determine whether listening to music has an effect on a student’s ability to learn. Design an experiment to help the psychologist answer the question. Copyright © 2016 Pearson Education, Inc. 28

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