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MATH 120 PRACTICE ASSESSMENT 2026
CERTIFICATION EVALUATION EXPERT
CHECKED
◉ Match each word or phrase. Answer: Provide numerical measures of individuals. The measures can be added or subtracted, and provide meaningful results. Quantitative Variable Allow for classification of individuals based on some attribute or characteristic. Qualitative Variable The characteristics of the individuals within the population. Variable Information that describes characteristics of an individual. Data Has either a finite number of possible values or countable number of possible values. The values of these variables typically result from counting.
Discrete Variable Has an infinite number of possible values that are not countable. The values of these variables typically result from measurement. Continuous Variable ◉ Number of pets. Answer: Is the variable qualitative or quantitative? The variable is quantitative because it is a numerical measure. ◉ Time to swim 100 meters. Answer: Is the variable qualitative or quantitative? The variable is quantitative because it is a numerical measure.
◉ Ages of children. Answer: Ratio ◉ The data on the right relate to characteristics of high-definition televisions A through E. Identify the individuals, variables, and data corresponding to the variables. Determine whether each variable is qualitative, continuous, or discrete.. Answer: What are the individuals being studied? (A) The high-definition television setups A through E. What are the variables and their corresponding data being studied? (A) Size (42, 54, 40, 40, 44), screen type (Projection, Plasma, Plasma, Projection, Plasma), and number of channels available (300, 107, 423, 270, 290) Determine whether each variable is qualitative, continuous, or discrete. Size is a continuous variable. Screen type is a qualitative variable. Number of channels available is a discrete variable.
◉ A news service conducted a survey of 1058 adults ages 18 years or older in a certain country, August 31−September 2, 2015. The respondents were asked, "Of every tax dollar that goes to the federal government, how many cents of each dollar would you say are wasted?" The four possible responses are that the federal government wastes less than 10 cents, between 11 cents and 25 cents, between 26 cents and 50 cents, or 51 cents or more. Of the 1058 individuals surveyed, 34 % indicated that 51 cents or more is wasted. The news service reported that 34 % of all adults in the country 18 years or older believe the federal government wastes at least 51 cents of each dollar spent, with a margin of error of 3 % and a 90 % level of confidence. Complete parts (a) through (e) below.. Answer: What is the research objective?
"jersey number" be? Now suppose the researcher felt that certain players who were of higher caliber received higher numbers. Does the level of measurement of the variable change? If so, how?. Answer: What is the level of measurement of the variable "jersey number" in the original scenario? Nominal Does the level of measurement of the variable change in the second scenario? Select the correct choice below and, if necessary, fill in the answer box within your choice. Yes, it changes to ordinal. ◉ Explain what is meant when it is said that "data vary". How does the variability affect the results of statistical analysis?. Answer: Saying "data vary" means that the values of the variable change from
individual to individual. In addition, certain variables can change over time for certain individuals. Because data vary, two different statistical analysis of the same variable can lead to different results. ◉ The methods of statistics follow a process. Place the processes in the correct order.. Answer: 1. Identify the Research Objective
Collect the Data Needed to Answer the Research Question(s)
Describe the Data
Perform Inference ◉ Match each phrase with its definition.. Answer: The values of the variable name, label, or categorize. In addition, the naming scheme does not allow for the values of the variable to be arranged in a ranked or specific order. Nominal level of measurement The values of the variable name, label, or categorize. In addition, the naming scheme allows for the values of the variable to be arranged in a ranked or specific order. Ordinal level of measurement
A(n) parameter is a numerical summary of a population. ◉ Fill in the blank. _________ are the characteristics of the individuals of the population being studied.. Answer: Variables are the characteristics of the individuals of the population being studied. ◉ Define statistics.. Answer: Statistics is the science of collecting, organizing, summarizing, and analyzing information to draw a conclusion and answer questions. In addition, statistics is about providing a measure of confidence in any conclusions. ◉ Match each word or phrase with its definition.. Answer: Occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study. Confounding An explanatory variable that was considered in a study whose effect cannot be distinguished from a second explanatory variable in the study. Confounding Variable
A researcher randomly assigns the individuals in a study to groups, intentionally manipulated the value of an explanatory variable, controls other explanatory variables at fixed values, and then records the value of the response variable for each individual. Designed Experiment An explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, this variable is typically related to other explanatory variables in the study. Lurking Variable A researcher measures the value of the response variable without attempting to influence the value of either the response or explanatory variables. That is, the researcher observes the behavior of individuals in the study and records the values of the explanatory and response variables. Observational Study ◉ Match each type of study to its definition.. Answer: Studies that are retrospecitve, meaning they require the researcher to look at existing records, or the subject to recall information from the past. Individuals who have certain characteristics are matched with those who don't. Case-control Study
◉ Eighty patients with stomach cancer are divided into two groups. One group receives an experimental drug to fight cancer, the other a placebo. After one year, the spread of the cancer is measured.. Answer: The study is an experiment because the researchers control one variable to determine the effect on the response variable. ◉ Researchers wanted to determine if there was an association between daily tea consumption and the occurrence of heart disease. The researchers looked at 93,577 women and asked them to report their tea-drinking habits. The researchers also determined which of the women had congestive heart failure. After their analysis, the researchers concluded that consumption of six or more cups of green tea per day was associated with a reduction in congestive heart failure.. Answer: (a) What type of observational study was this? Explain. This was a cross-sectional study because all information about the individuals was collected at a specific point in time.
(b) What is the response variable in the study? Is the response variable qualitative or quantitative? What is the explanatory variable? The response variable is whether the woman has congestive heart failure or not. The response variable is qualitative. What is the explanatory variable? The explanatory variable is consumption of green tea. (c) In their report, the researchers stated that "After adjusting for various demographic and lifestyle variables, daily consumption of six or more cups was associated with a 30% reduced prevalence of congestive heart failure." Why was it important to adjust for these variables? The researchers may be concerned with confounding that occurs when the effects of two or more explanatory variables are not separated or when there are some explanatory variables that were not considered in a study, but that affect the value of the response variable.
and the amount spent by the visitor. Complete parts (a) through (c) below.. Answer: (a) What is the explanatory variable in this study? Is it qualitative or quantitative? The explanatory variable is the web page design. The explanatory variable is qualitative. (b) What are the two response variables? For each response variable, state whether it is qualitative or quantitative. Select all that apply. A. One response variable is the number of items viewed. This response variable is quantitative. Your answer is correct. B. One response variable is the amount spent by the visitor. This response variable is quantitative. (c) Explain how confounding might be an issue with this study. Choose the correct answer below.
Since the designs are being tested with two different viewing devices, preferences depending on the viewing device may affect the response variables for those groups. ◉ esearchers wanted to know if there is a link between proximity to high-tension wires and the rate of leukemia in children. To conduct the study, researchers compared the rate of leukemia for children who lived within 1/2 mile of high-tension wires to the rate of leukemia for children who did not live within 1/2 mile of high- tension wires. The researchers found that the rate of leukemia for children near high-tension wires was higher than the rate for those not near high-tension wires. Can the researchers conclude that proximity with high-tension wires causes leukemia in children?. Answer: No, because this is an observational study. ◉ What is an observational study? What is a designed experiment? Which allows the researcher to claim causation between an explanatory variable and a response variable?. Answer: What is an observational study? B. An observational study measures the value of the response variable without attempting to influence the value of either the response or explanatory variables.
A lurking variable is an explanatory variable that was not considered in a study, but that affects the value of the response variable in the study. In addition, lurking variables are typically related to explanatory variables in the study. ◉. Answer: What is a case-control study? Case-control studies are observational studies that are retrospective, meaning that they require individuals to look back in time or require the researcher to look at existing records. Which is the superior observational study? Why? Neither study is always the superior to the other. Both have advantages and disadvantages that depend on the situation. ◉ What is a frame?. Answer: A frame is a list of the individuals in the population being studied. ◉ Define simple random sampling.. Answer: A sample of size n from a population of size N is obtained through simple random sampling if every possible sample of size n has an equally likely chance of occurring. The sample is then called a simple random sample.
◉ What does it mean when sampling is done without replacement?. Answer: Once an individual is selected, the individual cannot be selected again. ◉ As part of a college literature course, students must select three classic works of literature from the provided list and complete critical book reviews for each selected work. Write a short description of the processes that can be used to generate a simple random sample of three books. Obtain a simple random sample of size 3 from this list. Answer: *Number the books from 1 to 9 and use a random number table to produce 3 different one digit numbers corresponding to the books selected. *List each book on a separate piece of paper, place them all in a hat, and pick three. Use the portion of the random number table provided below to obtain a simple random sample of size 3
