Multiple Choice

1. What characterizes univariate data?

   It describes the relationship between a cause and an effect.

   It requires at least three variables to be collected for analysis.

   It involves analyzing the interaction between two distinct variables.

   It involves the collection and analysis of a single variable at a time.

2. A researcher collects the heights of $100$ randomly selected Grade 11 students. What kind of data is this?

   Bivariate data.

   Categorical data.

   Univariate data.

   Qualitative data.

3. How is bivariate data distinguished from univariate data?

   Bivariate data involves multiple samples, whereas univariate data uses a single sample.

   Bivariate data explores the relationship between two different variables, while univariate data examines one.

   Bivariate data uses a continuous scale, while univariate data uses a discrete scale.

   Bivariate data describes a single characteristic, while univariate data describes two characteristics.

4. A study measures both the number of hours students spend studying for a test and their corresponding test scores. What type of data is being collected?

   Multivariate data.

   Qualitative data.

   Bivariate data.

   Univariate data.

5. A meteorologist records the daily temperature and the amount of rainfall for a city over a month. What kind of data is being collected for analysis?

   Qualitative data.

   Bivariate data.

   Univariate data.

   Experimental data.

6. In a study investigating whether the amount of fertilizer used affects the height of a plant, which variable would be considered the explanatory variable?

   The amount of fertilizer used.

   The type of plant.

   The duration of the study.

   The height of the plant.

7. A scientist wants to determine if the number of hours a person sleeps influences their reaction time. Which variable is the response variable in this study?

   The age of the person.

   The person's reaction time.

   The number of hours a person sleeps.

   The type of activity performed.

8. What is the primary purpose of identifying an explanatory variable and a response variable in a statistical study?

   To describe the spread of a single variable's distribution.

   To investigate if changes in one variable cause or are associated with changes in another.

   To determine if the data is collected from a population or a sample.

   To categorize the data as either discrete or continuous.

9. A school counselor investigates if the number of extracurricular activities a student participates in affects their overall academic average. Identify the explanatory and response variables, respectively.

   Academic average, extracurricular activities.

   Student's grade level, academic average.

   Extracurricular activities, academic average.

   Number of students, extracurricular activities.

10. Which of the following scenarios would typically involve the analysis of bivariate data?

    Measuring the weights of all newborn babies in a hospital for a month.

    Examining the relationship between daily exercise time and blood pressure levels.

    Counting the number of students who prefer apples in a class.

    Recording the favorite color of each student in a survey.

11. A health study collects data on participants including their age, Body Mass Index (BMI), hours of sleep per night, and weekly exercise duration. If the researchers are specifically investigating whether a participant's weekly exercise duration influences their BMI, how should the data being analyzed for this specific investigation be classified, and what roles do the variables play?

    Bivariate data; both weekly exercise duration and BMI are response variables.

    Bivariate data; weekly exercise duration is the explanatory variable and BMI is the response variable.

    Univariate data; BMI is the explanatory variable and weekly exercise duration is the response variable.

    Univariate data; weekly exercise duration is the only variable of interest.

12. A study observed a strong positive correlation between the number of ice cream cones sold in a city and the number of drowning incidents reported in public pools during summer months. Which of the following is the most appropriate classification of these variables and their likely roles?

    Number of drowning incidents is the explanatory variable, and number of ice cream cones sold is the response variable, implying a counter-intuitive causal effect.

    Both variables are purely univariate, and their apparent relationship is coincidental without any underlying connection.

    Number of ice cream cones sold is the explanatory variable, and number of drowning incidents is the response variable, suggesting a direct causal link.

    The data is bivariate, but neither variable is likely explanatory for the other; instead, a confounding variable like ambient temperature likely explains the observed correlation.

13. A psychology experiment records the reaction time of participants to a visual stimulus (in milliseconds) and their self-reported stress level (on a scale of $1-10$) before the experiment. The researcher's immediate goal is to simply describe the distribution of reaction times for the group and the distribution of stress levels for the group, without initially exploring a relationship between them. How should the collected data be categorized for this specific descriptive purpose?

    The data is bivariate because there is an inherent, known psychological relationship between stress and reaction time.

    The data is univariate because, for this specific purpose, the two variables are being analyzed independently to describe their individual distributions.

    The data is multivariate because multiple pieces of information are collected from each participant.

    The data is bivariate because two different measurements are taken for each participant, implying a potential relationship.

14. A school district is exploring if the amount of funding allocated per student in schools correlates with the average standardized test scores of students in those schools. They hypothesize that higher funding *per student* leads to better academic outcomes. How should the variables in this investigation be defined and categorized?

    The amount of funding per student is the explanatory variable, and the average standardized test score is the response variable.

    Both the amount of funding per student and the average standardized test score are response variables, as they are both outcomes influenced by various policy decisions.

    The average standardized test score is the explanatory variable, and the amount of funding per student is the response variable.

    This is a univariate analysis, focusing solely on the distribution of school funding.

15. A study examines whether students who regularly participate in extracurricular sports (categorized as 'Yes' or 'No') tend to have a different average Grade Point Average (GPA) than those who do not. How should the variables for this study be correctly classified and their roles identified?

    This is a univariate study because the primary focus is on describing the distribution of GPA among students.

    Participation in extracurricular sports is the explanatory variable (categorical), and GPA is the response variable (quantitative).

    GPA is the explanatory variable, and participation in extracurricular sports is the response variable, implying GPA dictates participation.

    Both participation in extracurricular sports and GPA are response variables, as they are observed characteristics of students.

16. In an agricultural experiment, $100$ identical corn plants are grown under rigorously identical conditions (same soil type, consistent sunlight exposure, exact water regimen, constant temperature). The only factor varied by the researchers is the amount of a new liquid fertilizer applied to each plant. At the end of the growing season, the final height of each plant is measured. For this experiment, what are the primary variables being studied and their respective roles?

    The amount of fertilizer applied is the explanatory variable, and the final height of the plant is the response variable.

    The final height of the plant is the explanatory variable, and the amount of fertilizer applied is the response variable, suggesting plant height influences fertilizer use.

    This is a univariate study because all other environmental conditions are controlled, reducing variability.

    Soil type, sunlight, water, and temperature are all explanatory variables, while plant height is the response.

17. Which of the following statements provides the most accurate and comprehensive description of bivariate data?

    Bivariate data can only be analyzed if both variables are quantitative measurements on a continuous scale.

    Bivariate data primarily aims to describe the characteristics of a single variable within a specific population.

    Bivariate data always implies that one variable directly causes a change in the other variable.

    Bivariate data involves two distinct variables collected from the same individuals or observational units, with the central objective of exploring, describing, or explaining the relationship between these two variables.

18. An economist is conducting a historical study to investigate the relationship between a country's annual Gross Domestic Product (GDP) and its average national life expectancy over the past $50$ years. For each year in this period, they record both the country's GDP and its average life expectancy. How would this investigation be best described in terms of data types and variable roles?

    Both annual GDP and average national life expectancy should be considered response variables, as they are both complex outcomes influenced by numerous global and domestic factors.

    This is a bivariate study where annual GDP is the likely explanatory variable and average national life expectancy is the likely response variable, given typical economic and health policy frameworks.

    This is a univariate study focused primarily on the trend of GDP over time.

    Average national life expectancy is the explanatory variable, and annual GDP is the response variable, implying that life expectancy drives economic output.

19. A pharmaceutical company is designing a study to investigate the effect of different dosages of a new drug (measured in milligrams) on a patient's reduction in symptom severity (measured on a scale of $0-100$). Which statement correctly identifies the variables and their appropriate roles within this study design?

    This is a univariate analysis, as the study focuses primarily on the patient's symptom reduction.

    Both drug dosage and reduction in symptom severity are response variables, as they are both measured after administering the drug.

    Reduction in symptom severity is the explanatory variable because it is the observed outcome.

    The drug dosage is the explanatory variable because it is the manipulated factor presumed to influence the reduction in symptom severity.

20. A climate scientist collects the following data for $20$ different cities over a year: average annual temperature, total annual rainfall, elevation above sea level (in meters), and average annual particulate matter concentration. If the scientist then creates a scatter plot to visually observe if cities with higher elevations tend to exhibit lower average annual temperatures, how is the data used for this specific visualization and analysis best characterized?

    This is a bivariate analysis where total annual rainfall is the explanatory variable, because it often correlates with temperature.

    This is a multivariate analysis, as more than two types of data were initially collected for each city.

    This is a bivariate analysis where elevation above sea level is the explanatory variable and average annual temperature is the response variable.

    This is a univariate analysis of average annual temperature, as elevation is just a descriptive factor.