Collecting Statistical Data

blind study (13.6) census (13.1) chance error (13.4) clinical study (13.6) confounding variable 13.6 convenience sampling 13.2 controlled study (13.6) Word Bank: control group (13.6) data (intro) N-value (13.1) nonresponse bias (13.2) parameter (13.4) poll (13.2) population (13.1) Chapter 13: Collecting Statistical Data placebo (13.6) placebo effect (13.6) quota sampling (13.2) random sampling (13.3) respondent (13.2) response rate (13.2) sample (13.2) sample bias (13.4) sampling error (13.4) selection bias (13.2) statistic (13.4) statistics (intro) survey (13.2) treatment group (13.6) INTRODUCTION 1. ____STATISTICS________________ - the science concerning the collection, analysis, interpretation and presentation of data; it is the blending of two skills we learn in school – communicating and manipulating numbers 2. ____DATA______________________ - information or observations of a measureable event packaged in numerical form. Section 13.1 – POPULATION 3. _______POPULATION____________ - the group of individuals or objects on which data is collected 4. _______N-VALUE________________ - the number of individuals or objects in a population 5. _______CENSUS_________________ - the process of collecting data by going through every member of the population Section 13.2 – SAMPLING 6. ______SAMPLE__________________ - the subgroup of a population that is chosen to provide data on a population 7. ______SURVEY__________________ - the process of collecting data from a subset of the population 8. ______POLL_____________________ - the process of collecting data by asking questions 9. ______SELECTION BIAS__________ - a built-in tendency to exclude from the sample a particular group or characteristic of the population 10. ______RESPONDENT____________ - a person who responds to a survey or poll 11. ______RESPONSE RATE________ - the percentage of respondents out of the total sample who respond to a survey or poll 12. ___NONRESPONSE BIAS________ - the unintentional bias that is created by a low response rate 13. __CONVENIENCE SAMPLING___ - sampling that is dictated by what is easiest for the data collector and risks that the sample will not represent the population 14. ____QUOTA SAMPLING________ - sampling that systematically forces the sample to be representative of the population so that the proportion in each category of a sample is the same as the population Section 13.3 – RANDOM SAMPLING 15. ____RANDOM SAMPLING______ - sampling that uses the laws of chance (probability) to determine the selection of a sample; methods of this type of sampling can be simple (e.g. drawing names from a hat) or stratified in which the sampling frame is broken into categories called strata Section 13.4 – SAMPLING – TERMINOLOGY AND KEY CONCEPTS 16. _____PARAMETER_____________ - numerical information drawn from a population 17. _____STATISTIC_______________ - numerical information drawn from a sample; it is an estimate for the parameter of a population 18. ____SAMPLING ERROR________ - the difference between the parameter and the statistic used to estimate the parameter 19. ____CHANCE ERROR__________ - sampling error that is inherent in a sample that can only give approximate information about the population; this error is unavoidable but can be minimized with careful selection of the sample and the sample size. 20. ____SAMPLE BIAS_____________ - sampling error that is comes from selecting a bad sample that does not properly represent the population; this error can be eliminated by using proper methods of sample selection Section 13.6 – CLINICAL STUDIES 21. ____CLINICAL STUDY_________ - a study conducted to determine whether a single variable or treatment (e.g., a vaccine or drug) can cause a certain effect (e.g. a cure) 22. __CONFOUNDING VARIABLE__ - a variable that can cause the same effect as the variable under investigation 23. ___CONTROLLED STUDY______ - a clinical trial in which the subjects are divided into two different groups: the treatment group and the control group 24. ___TREATMENT GROUP________ - the group of subjects in a clinical trial who receive the actual treatment under investigation 25. ___CONTROL GROUP___________ - the group of subjects in a clinical trial who do not receive any treatment 26. ___PLACEBO EFFECT__________ - a confounding variable in which the idea alone that one is receiving a treatment produces positive results 27. ____PLACEBO_________________ - a fake treatment intended to look like the real treatment 28. ____BLIND STUDY_____ - a study in which the neither the members of the treatment group nor the members of the control group know which group they belong to; in a double-blind study, the researchers conducting the experiment also do not know which subjects are in which group Chapter 13: Collecting Statistical Data Practice Problems For #1 – 4: As part of a sixth-grade statistics project, the teacher brings to class a candy jar full of gumballs of two different colors: red and green. The assignment is to estimate the proportion of red gumballs in the jar. To do this, the jar is shaken well, and one of the students draws 25 gumballs from the jar. Of these, 8 are red and 17 are green. 1. (a) Describe the population for this survey. Gumballs in the jar Gumballs drawn by the student (b) Describe the sample for this survey. (c) Give the sample statistic for the proportion of red gumballs in the jar. 8/25 or 32% (d) Name the sampling method used for this survey. Simple Random Sample 2. Given that the total number of gumballs in the jar is 200, (a) give the sampling proportion for this survey (sample size to population). 25/200 = 12.5% (b) give the sample statistic for the number of red gumballs in the jar. 200*.32 = 64 red 3. Given that the total number of gumballs in the jar is 200 and the number of red gumballs is 50, (a) give the parameter for the proportion of red gumballs in the jar. 50/200 = 25% (b) give the sampling error, expressed as a percent. 32% - 25% = 7% (c) if the sampling error found in (b) a result of sampling variability or sampling bias? Sampling variability. Simple random sample do not suffer from selection bias. 4) (a) Compare and contrast the target (survey applies to) population and the sampling frame (actual subset of the population in the sample) for this survey. IDENTICAL = both consist of the jar of gumballs (b) What data collection method could be used to find the exact value of the parameter? Census For #5 – 7: A city has 8325 registered voters and the mayoral election has three candidates: Smith, Jones, and Brown. The day before the election, a telephone poll of 680 randomly chosen registered voters produced the following results: 306 people would vote for Smith, 272 for Jones, and 102 for Brown. 5. (a) Describe the population for this survey. 8325 REGISTERED VOTERS (b) Describe the sample for this survey. 680 REGISTERED VOTERS WITH TELEPHONES (c) Give the sampling proportion for this survey. 680/8325 = .08168 or 8.17% (d) Give the sample statistic estimating the percentage of the vote going to Smith. 306/680 = 45% 6. Given that the actual election Smith received 42%, Jones 43%, and Brown 15% of the vote, find the sampling errors in the survey expressed as percentages. Smith: Sample = 306/680 = 45% Actual = 42% Sampling Error = 3% Jones: Sample = 272/680 = 40% Actual = 43% Sampling Error = 3% Brown: Sample = 102/680 = 15% Actual = 15% Sampling Error = 0% 7. Do you think that the sampling error in this example is due to chance error or to sample bias? Explain. Chance Error: Because 100% response rate and random selection of sample For #8 – 10: That 1250 students at a high school are having an election for Homecoming King. The candidates are Tomlinson (captain of the football team), Garcia (class president), and Marsalis (member of the marching band). At the football game a week before the election, a preelection poll is taken of students as they enter the gates. Of the students that attended the game, 203 planned to vote for Tomlinson, 42 for Garcia, and 105 for Marsalis. 8. (a) Describe the sample for this survey. 350 students attending the football game (b) Give the sampling proportion for this survey. 350/1250 = 28% (c) Name the sampling method used for this survey. Convenience Sampling (at a football game  convenient but doesn’t allow all students to be polled) 9. (a) Compare and contrast the population and the sampling frame for this survey. Population = all 1250 students at the high school, Sampling frame = only 350 students who attended a specific football game. (b) Is the sampling error a result of sampling variability or sampling bias? Explain. SAMPLING BIAS. Not all students may attend the football game. Football fans may be more biased toward a football player. 10. (a) Give the sample statistics estimating the percentage of the vote going to each candidate. Tomlinson = 203/ 350 = 58% Garcia = 42/305 = 12%, Marsalis = 105/305 = 30% (b) A week after this survey, Garcia received 51% of the vote, Marsalis got 30% and Tomlinson got 19%. Find the sampling error errors in the survey expressed as percentages. Tomlinson = 39% = 58% - 19% Garcia = 39% = 51% - 12% Marsalis = 0% = 30% - 30% CHAPTER 13 MULTIPLE CHOICE PRACTICE PROBLEMS For #1 – 11: A 6th grade teacher brings a container with 300 red marbles and 500 white marbles which are thoroughly mixed. To figure out how many marbles in the container are red without actually counting them all, a student randomly draws 40 marbles from the container and 16 are red. 1) The data collection method in this example can be described as A. census B. Survey C. Clinical Study D. Controlled Study 2) The target population consists of A. 800 marbles in the container. C. 40 marbles drawn by student 3) The N-value for this population is B. 300 red marbles in container. D.16 red marbles drawn by student. A. 16 B. 40 C. 300 D. 800 4) The sample consists of A. 800 marbles in the container. C. 40 marbles drawn by student B. 300 red marbles in container. D.16 red marbles drawn by student. 5) The sample proportion is B. 51/3% A. 5% C. 131/3% D. 37.5% 6) Suppose that the student is given the N-value. What is a reasonable estimate for the number of red marbles in the container? A. 107 B. 300 C. 320 D. 480 7) Suppose that the student is given the N-value. What is a reasonable estimate for the number of white marbles in the container? A. 107 B. 300 C. 320 D. 480 8) The sampling error is A. 1% B. 2.5% C. 4% D. 62/3% 9) The sampling error is most likely a result of A. confounding variable. C. sampling bias B. nonresponse bias D. sampling variability 10) The sampling frame for this survey A. is smaller than the target population. C. is larger than the target population. B. is the same as the target population. D. contains members that re not in the target population. 11) The sampling method used in this example is called A. stratified sampling. B. Quota sampling. C. simple random sampling. D. Random sampling (not simple) For #12 - 15: A child has an enormous jar in which she has been saving all of her spare change. In order to determine exactly how much money she has in the jar, she dumps all the coins on the floor and counts them as 180 pennies, 120 nickels, 100 dimes, and 80 quarters. 12) The data collection method used in this is sample is called A. Survey B. Census C. Controlled Experiment D. Random Sampling 13) In the statement “There were 80 quarters in the jar”, the number 80 is A. Parameter B. Statistic C. Population D. Confounding Variable 14) If the population in this example is defined to be all the coins in the jar, the N-value is A. 180 B. 120 C. 100 D. None 15) If the child were to grab a handful of 48 coins at random from the jar, how much money should she expect it to be worth? A. $3.78 B. $4.80 C. $4.92 D. $39.60 # 16 – 18: A farmer wishes to work out the average milk yield in his heard that consists of an equal number of Ayrshire, Friesian, Galloway, and Jersey cows. 16) Suppose the farmer divides up his herd into the four sub-groups and randomly samples 3 cows from each subgroup. What type of sampling is being used? A. Quota Sampling B. Simple Random Sampling C. Stratified Sampling D. Convenience Sampling 17) Suppose the farmer doesn’t know which cows are which type or that there are equal percentages of each type in his herd. He chooses 3 cows that heels are representative of each type to be in his sample. What type of sampling is being used? A. Quota Sampling B. Simple Random Sampling C. Stratified Sampling D. Convenience Sampling 18) Suppose the farmer samples the 12 cows in his barn that are closest to where he enters the barn. What type of sampling is being used? A. Quota Sampling B. Simple Random Sampling C. Stratified Sampling D. Convenience Sampling #19 - 24: In order to determine the effectiveness of a new vaccine that is alleged to cure “math anxiety”, an experiment was conducted. One thousand volunteer college students enrolled in math courses across the US were chosen and broken into two groups. Those enrolled in calculus or higher were given the real vaccine, and those in remedial and basic math courses were given a fake vaccine. None of the students knew whether they were being given the real or fake vaccine, but the researcher conducting the experiment knew. At the end of the semester the students were given a test that measured their level of math anxiety. The students in the treatment group showed significantly lower levels of math anxiety than those in the control group. On the basis of this experiment the vaccine was advertised as being highly effective in fighting math anxiety. 19) The sampling frame in this experiment consists of A. treatment and control groups B. All US College students C. All US College students enrolled in math classes D. All students that suffer from “math anxiety” 20) The target population in this experiment consists of A. treatment and control groups B. All US College students C. All US College students enrolled in math classes D. All students that suffer from “math anxiety” 21) The control group in this experiment consists of A. 1,000 volunteer college students B. students given real vaccine C. students given fake vaccine D. no control group because of it used volunteers 22) This experiment can best be described as a A. double blind randomized controlled C. blind randomized controlled B. double blind controlled placebo D. blind controlled placebo 23) The results of this experiment should be considered unreliable because A. only college students used. B. treatment/control groups were not the same size. C. sample was too small D. treatment/control groups represented very different segments of population 24) Which of the following is the most likely confounding variable for this experiment? A. student’s background in mathematics B. student’s grade level C. the type of college attended D. student’s gender