Chapter 1 Lab(1)

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Mathematics

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Feb 20, 2024

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MAT 157 Chapter 1 Lab Statistics Unit 1, Chapter 1 Lab Part 1 : Levels of Measurement, Types of Data *Determine the level of measurement as nominal (n), ordinal (o), or interval/ratio (i/r) for the following types of data. *Then, determine if the data would be quantitative/numeric (N) or categorical/qualitative (C). *IF it is quantitative/numeric indicate if it is discrete (d) or continuous (c). 1) Age: R,N,C 2) Height: R,N,C 3) Class standing (1=freshman, 2=sophomore, 3=junior, 4=senior) O,C 4) Gender: n,C 5) Length of time it takes to get to school: i/r,N,C 6) High temperature for the day to the nearest degree: i/r,N,D 8) Number of siblings: R,N,d 9) Country of birth :n,C, 10) Eye color: n,C 11) Level of satisfaction with bookstore (1 = very high, 2, 3, 4 or 5 = very low) o,C 12) Income (reported as exact $s—no cents) i/r,N,d 13) Zip code n,C 14) GPA i/r,N,d 15) Perceived speed of computer (1=very slow, … , 7=very fast) o,C 16) Heart rate (beats per minute) i/r,n,c 17) Star rating of a movie (4 stars…etc) n,C 18) Write down an original that would be quantitative/numeric, discrete, and interval. Weight on a digital scale P a g e | 1

MAT 157 Chapter 1 Lab 19) Write down an original topic other that would be quantitative/numeric, continuous, and interval/ratio. The time it takes to finish a 100 meter dash Part 2 : Sampling Methods. Determine which sampling method(s) is/are used in each scenario. Simple random, systematic, convenience, stratified, cluster, or none. A) A teacher has the names of her students on popsicle sticks in a cup. She draws 4 sticks from the cup and asks those 4 students a question. Simple Random B) To gather information about the current attitudes of the local constituents regarding a levy, a company used a random number generator to select which individuals to talk to. Simple random C) The student activity council wants to find out the student body’s opinion regarding creating an outdoor study space. Members of the council are randomly assigned a classroom to visit and then they give all students in that classroom a survey. Cluster D) A radio show host did a poll where listeners could go to the radio host’s Facebook page and cast their vote as to which brand of potato chips they prefer. Convienence E) The CEO of a grocery store wants to find out information regarding their customers’ shopping experiences. They pose a researcher as a cashier and she is instructed to ask every third person a particular question regarding the customer’s shopping experience. systematic F) A city council is trying to determine the use of a large sum of money that was left to them by a recently deceased resident. The council decides that they will survey a variety of individuals. First, the council decides that they want to survey people from the following age groups: 18 – 25 years, 26 – 35 years, 36 – 45 years, 46 – 60 years, 60+ years. Once they have the population categorized by age, they use an alphabetical list for each category and have council members call every 10 th person on the list. Stratified and systematic G) Describe the difference between stratified and cluster sampling. The difference between stratified and cluster sampling is that With stratified they pick people by characteristics whilw mwith cluster they pick everybody. P a g e | 2

MAT 157 Chapter 1 Lab P a g e | 3

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MAT 157 Chapter 1 Lab Part 3 : Vocabulary and Sampling Methods. I dentify the following A). The population B) The sample C) The sampling method(s) used. 1. You are interested in what the students at a private school think about changing the uniform requirement from white polos to red, white, or gold polos. You decide to select 12 of the 35 homeroom groups to ask to take your survey. a. Private school students b. .12 of the 35 homeroom groups c. cluster 2. A congressman wants to find out what the voters in Sac county think about the oil pipeline that is scheduled to come through Iowa farmland. He has his secretary generate a list of all registered voters in Sac County and calls every 20 th person on the list. a. .Voters b. .the 20 th persons that respond c. .systematic 3. A city is considering putting in a public pool. They want to determine the public’s views on the project. A city councilman goes to a local grocery store one day and asks 30 people their opinions. a. .the public b. .30 people at the grocery store c. .convenience 4. A college algebra professor wants to sample his students’ perspectives of math before and after they take his course. He generates a class list, by grade (freshmen, sophomore, junior, senior) and then uses a random number generator to select 10 students from each grade. a. .students b. .10 students from each grade c. .stratified 5. The RA in a dorm at a small college wants to find out which events the residents would be most interested in attending throughout the year. She knows there are 128 freshmen, 112 sophomores, 96 juniors, and 48 seniors living in her dorm. She decides that she is going to ask 43 of the freshmen, 33 of the sophomores, 24 of the juniors, and 6 of the seniors. a. .residents b. .The number of students of each class that the ra decided to pick c. .Stratified P a g e | 4

MAT 157 Chapter 1 Lab Determine which sampling method(s) you believe would be best. Then determine possible flaws with the method(s). 6. In the article, “Ghosts of Speciation Past” (Nature, Vol. 435, pp 29-31), Kocher looks at the origins of a diverse flock of cichlid fishes in the lakes of southeast Africa. Suppose that you wanted to select a sample from the hundreds of species of cichlid fishes that live in the lakes of southeast Africa. Which type of sampling design would you use? Explain. I believe cluster would be the best method because it would not be practical to go to all the lakes of Africa . The possible problem that you could run into would be that some species could possibly not be found in the region you are sampling from. 7. An experimenter wants to estimate the average water consumption per family in a large city. Which type of sampling design would you use? Explain. Simple random would be the best method to use because you could obtain averages from the water company but down fall would be families living in apartment complexes because the utility company may not have the breakdown of the water consumption by individual apartment 8. An industry consists of many small plants located throughout the United States. An executive wants to interview employees regarding their opinions about the industry vacation policy. Which type of sampling design would you use? Explain. In my opinion it would be cluster systematic I would pick every 10 th plant and interview a certain number of people by employment status. the downfall would be depending on employment status you would get different responses because managers , administration and laborers would have different opinions on the package. Part 4 : Blinding, Confounding, Vocabulary. In each description below determine the type of study (observational or experiment).  IF observational, determine the type of observational study (retrospective, cross- sectional, prospective) and any potential pitfalls that could lead to invalid conclusions.  IF experimental, determine sources of possible confounding and if there was single blinding, double blinding, or no blinding, Scenario 1 : In a new study, it was found that women that used bleach (or cleaners that contain bleach) for regular cleaning were 3 times more likely to have asthma than women that did not use bleach for regular cleaning. Women were given surveys over the course of a year regarding their cleaning habits and products used. Each woman was also tested during this time for asthma by a health professional. This is a prospective observational study, the possible pitfalls would be it does not define what is “regular” cleaning and just because these women used bleach doesn’t necessarily mean that this is the root cause of the asthma, because I am sure a lot people that do not use bleach have been diagnosed with asthma too. The root cause of the asthma could very well be caused by dust and mold. P a g e | 5

MAT 157 Chapter 1 Lab Scenario 2 : A pharmaceutical company hired an independent firm to test the effectiveness of a new drug on treating muscular sclerosis. The individuals with muscular sclerosis from across the Midwest were assigned to different treatment groups based on the stage of the disease. Each treatment group was either given a high dose, low dose, or a placebo dose—but the groups did not know which treatment they were given. Medical professionals measured the severity, stage, and progression of the disease in each individual over the course of the study, but the medical professionals did not know which groups each patient was a part of. It was found that 74% of patients saw a reduction in the symptoms of the disease while using the new drug. This is an experiment and the confounding is that the groups were based on the different stages of the disease other than random because if the group with the most extreme case was given the placebo the study would show way different numbers than if the mildest case would be given the placebo dose. This is what we call a double blinding experiment because no one knows the dosages but the researcher. General: What is the purpose of using blinding in research? What can be done to reduce confounding in research? The purpose of the blinding in research is to prevent what we call the placebo effect which is pretty much one “thinks” a drug is working or is psychologically manipulating the results and progress based on expectation rather than actual results. To reduce confounding’s participants should be placed into groups by random assignment. Part 5: Surveys. A. Go to Blackboard  course content  unit 1  chapter 1  supplement. Open the item titled Surveys. Determine how these two surveys are related to the topics discussed in chapter 1 and why the individuals that created the survey likely created them in this way. Give specific details/terms. These are very biased surveys that are full of loaded questions to try to get a certain result out of the sample that is surveyed. B. Pick a topic that is currently “controversial” in your school/community/religious group/etc and write a question regarding that topic that is 1) biased in favor of the topic 2) biased opposed to the topic 3) not biased. (Example: In my home town they are trying to get funding for a walking/biking trail…. 1). Do you think the health benefits, safety benefits, and value added to our town are valuable assets to consider when considering the installation of a new, modern, and safe walking/biking trail? 2). Are you willing to have your taxes increase to pay the outlandish cost of putting in a trail that will hardly be used? 3). Do you support the funding of the walking/biking trail? 1). Is building a recreational center that is going to benefit the elderly and youth by giving another resource to the community that promotes health and wellness worth a couple extra dollars towards property taxes. P a g e | 6

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MAT 157 Chapter 1 Lab 2). Is the small 800 square foot rec center worth wasting millions of hard earned tax dollars ? 3).Do you support the funding of the new recreational center? Part 6 : Media Claims In BB there is (same folder as part 5) open the item titled Media Claims and pick a few links to look at with your group. See if you can pull out any of the important “prepare” items in the statistical process (What do the data represent? What was the purpose/goal of the study? What is the source of the data? Does it seem to be reputable or potentially biased? What is the sampling method used? Would this likely be a representative sample?) Why might this information not be readily available in these articles? The goal of these studies seemed to be to mislead the public into thinking that certain products are harmful then try to sell them a product that is free from that danger or factor that is being explained in the article the sampling method is convenience. While the first two articles are unbiased because they have explanations de bunking these myths Part 7: Real Life Research -Access DMACC’s Library site. -Select “Find Articles” -Enter a topic of interest in the search bar (I did “organic foods” as my example below) -Select one of the articles that seems to be an experiment/study and has “View full text” as an option. Find the following information for your articles; all of which is associated with the “prepare” component of statistics: 1) What do the data represent? What is the type of data (ratio/interval, etc.) The data represents the literacy of blind or visually impaired. The type of data was nominal . 2) What was the purpose/goal of the study? The purpose of the data is to see what percentage of students that were blind can read braille 3) What is the source of the data? Does it seem to be reputable or potentially biased? It seems reputable because a lot of the references are credible and the writers of the article would have nothing to gain by being dishonest 4) What is the sampling method used? Would this likely be a representative sample? The sample method seems to be cluster with simple random because the sample group has to blind or visually impaired enough to have to use braille P a g e | 7

MAT 157 Chapter 1 Lab 5) What might be one source of confounding? I could not think of a confounding source 6) Were the results statistically significant? Were the results practically significant? I do not know how to answer that because this is an observational study it seems like My EXAMPLE P a g e | 8

Chapter 1 Lab(1)

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