AP Statistics FRQ Room

Analysis of Weather Data: Daily Rainfall

A meteorologist recorded daily rainfall (in mm) over a month and summarized the data in the followin

App Usage: Comparing Two Advertising Campaigns

A mobile app company ran two advertising campaigns. In Campaign 1, 400 out of 800 users clicked the

Bootstrap Simulation of the Sampling Distribution of the Median Salary

Given the salary data $$\$3000$$, $$\$7000$$, $$\$15000$$, $$\$22000$$, $$\$23000$$, and $$\$38000$$

Calculating Variance and Standard Deviation for Book Counts

The numbers of books read by 10 students in a month are recorded as: {3, 4, 2, 5, 6, 4, 3, 3, 4, 5}.

Car Price and Mileage Regression Analysis

A used-car dealership analyzes data from 80 vehicles to predict the selling price (in thousands of d

Comparing Sampling Distributions from Populations with Different Variances

Two independent populations have identical means but different variances: Population X has $$\sigma^

Cumulative Frequency Analysis: Graduation Ages

A cumulative frequency graph of graduation ages is provided. From the graph, it is observed that the

Daily Step Count Hypothesis Test

A fitness app collects data from a random sample of 40 users. The sample shows an average daily step

Digital vs. Traditional Lesson Impact on Class Attendance

A school district is testing whether interactive digital lessons lead to higher class attendance tha

Distribution Shape and Confidence Interval Interpretation

A survey of 100 car owners reveals that the cars’ mileages have a mean of $$60000$$ miles and a medi

Dotplot Representation of Home Run Distances

A dotplot displays the following frequencies for home run distances (in feet): • 387 appears once •

Effect of Skewness on the Sampling Distribution of the Mean

A company tracks daily website visits which are heavily right-skewed. A data analyst simulates drawi

Effectiveness of a New Drug

A clinical trial is conducted to evaluate the effectiveness of a new drug in improving patient outco

Employee Salary Adjustments

A company has six employees with the following salaries (in dollars): $$\{3000, 7000, 15000, 22000,

Event Attendance by Invitation Type

An event organizer tracked attendance based on invitation type (Digital, Paper) and the outcome (Att

Examining Data Variability in Sports Statistics

A boxplot summarizes the points per game for a basketball player over a season with the following va

First Defective Product: Geometric Distribution

In a factory, each product has a 3% chance of being defective. Products are inspected sequentially u

Interpreting Boxplots for Salary Data

A survey of 50 teachers provided salary data summarized in the following boxplot: - Minimum: $30,0

Interquartile Range and Boxplot Construction

Given the dataset: {12, 15, 16, 18, 20, 22, 25, 27, 30, 35}, perform an analysis of its distribution

Leadership Training and Employee Satisfaction

A business management study is investigating whether participation in a leadership training workshop

Lottery Ticket Analysis

The probability of winning on a single lottery ticket is $$0.001$$. A person buys tickets one after

Marketing Campaign Reach by Region

A company tracked responses to a marketing campaign in two regions (Region 1 and Region 2) categoriz

Medication Efficacy in Reducing Blood Pressure

A research team is designing an experiment to evaluate the efficacy of a new preventative medication

Mobile Device Battery Life

The battery life of smartphones is normally distributed with a mean of $$10$$ hours and a standard d

Normal Distribution of Taxi Mileage

Taxicabs in a city are driven an average of $$75000$$ miles per year with a standard deviation of $$

Nutrition Study: Effects of Diet on Weight Loss

A nutritionist intends to study whether different diets lead to different average weight losses over

Online Examination Scores

Scores on an online examination are normally distributed with a mean of $$75$$ and a standard deviat

Parent Survey on School Length

A survey of 2000 parents asked which school year length they preferred. The following table summariz

Product Return Rates Across Regions

A company tracks product returns across four regions (North, South, East, West) with outcomes 'Retur

Public Opinion on School Length: Categorical Data Summary

In a survey of 2000 parents regarding their preference for the length of the school year, the respon

Social Media Platform Usage by Gender

A survey of 400 respondents recorded their preferred social media platform (Platform X or Platform Y

Stem-and-Leaf Analysis of Ages

A stem-and-leaf plot displays the ages (in years) of participants in a study as follows: 2 | 1 3 5

Stemplot Construction: Analyzing a Data Set

A dataset of 11 numbers is provided as follows: {12, 15, 15, 17, 17, 18, 20, 22, 22, 23, 25}.

Study Program Effectiveness Hypothesis Test

A researcher wants to determine if a new study program increases test scores. In a random sample of

Advertising Spend and Sales Revenue

A company collected monthly data over one year on its advertising expenditure (in thousands of dolla

Analysis of Marketing Campaign Data: Sales vs. Advertisements

A company conducted a marketing campaign across several regions and recorded the amount spent on adv

Assessing Scatterplot Patterns: Nonlinear Relationships

A health study investigates the relationship between the number of hours of exercise per week (X) an

Chi-Square Analysis for Dietary Habits and Exercise Frequency

A nutrition study classifies 300 individuals by their dietary habit (Vegetarian, Non-Vegetarian) and

Comparing Regression Lines With and Without an Influential Point

A company collected data on its monthly sales (Y, in millions of dollars) and advertising spending (

Consumer Beverage Preference Analysis

A fast‐food restaurant collected data on customer ordering preferences regarding dining style (Dine‐

Contingency Table Analysis: Cuteness Factor Study

In a study on the Cuteness Factor, 250 volunteers were shown pictures from three categories: Cute An

Cuteness Factor Study Revisited

A Japanese study collected data on 250 volunteers who were shown pictures of cute baby animals, adul

Daily Screen Time and Sleep Quality

A sleep study on 60 adults collected data on daily screen time (in hours, explanatory variable) and

Effects of Dropping a High-Leverage Observation

A dataset of 12 observations is used to fit a linear regression model predicting a response variable

Fitness Tracker Analysis

A fitness center collected data from individuals using fitness trackers, recording daily steps (x) a

Fitness Tracker: Step Count vs Active Minutes

A fitness tracking app collected data from 50 users on daily step count (in thousands) and active mi

Impact of a New Study App on Academic Performance

A technology company has developed a new study application intended to improve academic performance.

Impact of Sample Size on the Sampling Distribution of the Sample Mean in Two-Variable Data

A dataset containing paired observations of hours of exercise (x) and minutes of sleep (y) is used i

Neighborhood Safety Survey

A community survey collected data on residents' sense of safety based on their neighborhood type (Ur

Pharmaceutical Dosage Testing

A pharmaceutical company produces tablets designed to contain an active ingredient with a prescribed

Predicting Student Exam Scores from Study Hours

A researcher investigates the relationship between the number of hours a student studies (x) and the

Relationship between Study Hours and Test Scores

A study investigates the relationship between the number of hours students study per week and their

Residual Analysis in House Price Prediction

A real estate analyst develops a linear regression model to predict house prices (in $1000s) from ho

Restaurant Service and Tipping

A restaurant manager collected data on the wait time (in minutes) experienced by customers and the c

Simulating the Sampling Distribution of the Sample Range in Bivariate Data

A researcher is interested in exploring the sampling distribution of the range of response variable

Simulation-Based Investigation of Chi-Square Distribution in Two-Way Tables

A researcher is interested in the chi-square test for independence in a two-way table. To understand

Tech Company Productivity Analysis

A tech company collected data on the number of programming hours (x) and the number of bugs fixed (y

Voter Approval Polling

Preliminary polls indicate that 45% of voters approve of a candidate. A random sample of $$200$$ vot

Website Click-Through Rate

An online advertisement has a click-through probability of $$0.15$$ for each visitor. Suppose that 5

Analysis of Boxplots from an Experiment on Pulse Rates

Researchers conducted an experiment comparing the effects of three beverages (coffee, caffeinated co

Analysis of Product Return Rates: Online vs. In-Store

A retailer wants to compare product return rates between online and in-store purchases. Among online

Central Limit Theorem and Coffee Consumption

In a certain region, the average daily coffee consumption is 3 cups with a standard deviation of 1 c

Central Limit Theorem Demonstration Through Simulation with an Exponential Population

A researcher is interested in the Central Limit Theorem (CLT) and performs a simulation by drawing s

Commute Time and Job Satisfaction

A consulting firm conducts a study to examine whether longer commute times (in minutes, x) are assoc

Comparing Disease Incidence in Two Regions

A public health study investigated the incidence of a particular disease in two regions. In Region A

Comparing Test Scores Between Two Teaching Methods

A school is evaluating two different teaching methods. Group A, using Teaching Method A, had 25 stud

Evaluating the Sampling Frame in an Urban Survey

A research team plans to survey residents of a large urban area on community services. They initiall

Experimental Design: Evaluating a Review Course for SAT Scores

A study aims to evaluate whether a new SAT review course improves student scores. Students are rando

Factorial Experiment on Study Hours and Tutoring

A study is conducted to examine the effects of study hours and tutoring on student test scores. Stud

Heart Rate Recovery and Fitness Level

In a cardiovascular fitness study, researchers examine if higher fitness levels (measured by a fitne

Impact of a New Diet on Blood Pressure

A health clinic is investigating whether a new diet can reduce systolic blood pressure. Patients are

Impact of a Training Program on Employee Productivity

A company measured employee productivity before and after a new training program. Two independent sa

Impact of Sample Size on Confidence Interval Width

Consider two studies estimating the mean of a population, both with a known population standard devi

Integrating Surveys and Observational Studies in Urban Environmental Research

An urban environmental research team is investigating the relationship between urban tree cover and

Investigating Voluntary Response Survey Bias

A mid-sized university is conducting an online survey about campus safety. The survey is distributed

Matched Pairs Design in Educational Research

A school district is evaluating two teaching methods by having the same students experience both met

Measurement Reliability in Climate Data Collection

A climate study collects rainfall data from multiple sensors distributed across a region. The sensor

Mobile App User Engagement

A mobile app company uses a simple random sample of 100 users to estimate the average daily usage ti

Observational Study on Dietary Habits and Exam Performance

A high school is interested in studying the relationship between students' dietary habits and their

Random Assignment in a Placebo-Controlled Medical Trial

A medical researcher plans a clinical trial to test the effectiveness of a new drug for migraine rel

Retail Store Checkout Efficiency Study

A study compared the average waiting time at checkout between two methods in a retail store. For the

Retrospective Study on Environmental Exposure and Health Outcomes

A public health researcher is studying the relationship between long-term exposure to poor air quali

Screen Time and Anxiety Levels

A psychologist studies the relationship between daily screen time (in hours, x) and self-reported an

Smartphone Usage and Sleep Quality

Examine the relationship between smartphone usage and sleep quality among college students. Research

Study Habits and GPA: A Regression Analysis

A university researcher is examining the relationship between students' weekly study hours (x) and t

Systematic Sampling for a School Survey on Sports Participation

A high school with 500 students wants to survey opinions about sports participation. The principal d

Volunteer Firefighter Response Times

A prospective study of volunteer firefighter response times records data from 45 incidents. The samp

Work-from-Home vs. In-Office Job Satisfaction

A human resources study surveyed job satisfaction among employees working from home and those workin

Apartment Rental Prices Estimation

A real estate researcher is studying monthly apartment rents in a metropolitan area. In a random sam

Carnival Game Payoff Transformation

In a carnival game, the payoffs are: $$2$$ dollars with probability $$0.5$$, $$5$$ dollars with prob

Comparing Consumer Spending at Two Malls

Two shopping malls record the average spending per visitor. Mall A has a sample of 100 visitors with

Comparing Simulation Results for Rainy Days

A simulation study recorded weather in two cities over a 30-day month. The results are as follows:

Customer Satisfaction Survey

A retail company conducted a customer satisfaction survey both online and in-store. The results are

Defect Rate Comparison between Two Factories

A manufacturing company is studying defect rates in two of its factories. Factory 1 produced 1000 it

Defective Lightbulbs: A Binomial Distribution Problem

A lightbulb has a $$0.1$$ probability of being defective, and the outcomes are independent. Analyze

Drug Effectiveness Study

Researchers conducted a clinical trial comparing a new drug to a placebo. The recovery outcomes are

Effects of Outliers on Sampling Distributions

A simulation study involves drawing samples from a dataset that contains outliers. For each sample,

Engine Size and Fuel Efficiency Regression Analysis

A study investigates the relationship between engine size (in liters) and fuel efficiency (in miles

Evaluating a New Teaching Technique in High School

A school district is testing a new interactive teaching technique against the traditional method. Ce

Fitness Class Participation by Age Group

A gym surveyed 300 members about their preferred fitness class types. The results by age group are d

Impact of Advertising on Consumer Behavior

A marketing firm investigated the effect of advertisement exposure on purchasing decisions. The foll

Lottery Ticket Expected Outcome

A lottery ticket costs $2. The possible outcomes are: win $100 with probability 0.01, win $20 with p

Restaurant Orders by Meal Type and Tip Size

A restaurant collected data on tip sizes based on whether the order was dine-in or take-out. The res

Restaurant Tip Percentage Analysis

A restaurant manager claims that the average tip percentage is 18%. To test this claim, a random sam

Sampling Distribution from a Triangular Population

A simulation is performed where samples are drawn from a triangular distribution defined on the inte

Sampling Distribution of the Sample Mean from a Normal Population

A simulation experiment draws repeated random samples from a normally distributed population with $$

Sampling Distribution of the Sample Median from a Skewed Distribution

A simulation is conducted by drawing samples from a right-skewed distribution. For each sample, the

Simulated Binomial Sampling Distribution

A simulation experiment involves performing 20 independent Bernoulli trials with a probability of su

Simulated Sampling Distribution of Survey Proportions

A researcher simulates survey responses where each respondent answers 'Yes' or 'No' with a true prob

Student Majors and Graduation Outcome

A university tracked graduation outcomes for 300 students by major. The summarized data is provided

Student Testing Strategy and Scores Analysis

A standardized literacy test consists of 100 multiple-choice questions. When uncertain, test takers

Transformation of Payout Values

A game machine produces a random payout $$X$$ with a mean of $5 and a standard deviation of $3. A re

Urban Traffic Volume and Air Quality

City officials are studying the impact of traffic volume on air quality across several neighborhoods

Weather Temperature and Ice Cream Sales Regression Analysis

A vendor investigates the relationship between daily temperature (in °F) and ice cream sales (in dol

Yearly Savings and Investment Return Regression Analysis

A financial analyst studies the effect of yearly savings (in thousands of dollars) on the rate of in

Assessing the Conditions for the Central Limit Theorem

A production facility records the number of widgets produced per day by a machine. The daily product

Assessing Variability in a Manufacturing Process

A factory produces 1-liter plastic bottles with the volume of each bottle normally distributed aroun

Central Limit Theorem in Action: Distribution of Household Incomes

In a large metropolitan area, household incomes are highly skewed. A research team takes repeated ra

College Major and Internship Experience

A university conducted a survey on students' internship experiences across different majors. The tab

Comparing Clinical Trial Drug Effects

In a clinical trial, two drugs are used to lower blood pressure. Drug A produces an average reductio

Comparing Customer Satisfaction Among Two Stores

A retail chain conducts a study comparing customer satisfaction levels. In store A, 85% of customers

Effect of New Teaching Method on Student Scores

A school district is testing a new teaching method. Two groups of students are studied: a control gr

Employee Productivity by Shift

A company is examining the relationship between work shift (Morning vs. Evening) and productivity le

Environmental Concerns by Community Type

A survey was conducted to assess environmental concerns among residents in different community types

Evaluating Biased and Unbiased Estimators

A quality control manager is evaluating five different estimators (labeled A through E) for estimati

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

In a survey, it is found that 40% of respondents own a smartphone. A random sample of 200 respondent

Financial Returns: Biased vs. Unbiased Estimators

Investment analysts use two estimators to predict the expected return of a financial asset. Estimato

Genetic Mutations in New Fathers

It is estimated that 40-year-old men contribute on average $$65$$ genetic mutations to their offspri

Hypothesis Testing for a New Drug's Effect on Blood Pressure

A clinical trial is conducted to test the claim that a new drug reduces blood pressure by 10 mmHg. I

Manufacturing Process Consistency and Variability

A manufacturer recently implemented a new process intended to reduce variability in product weights.

Movie Theater Attendance by Genre Preference

A movie theater analyzed attendance frequency based on movie genre preference. The table below categ

Sample Variance Distribution in Produce Weights

A study measures the weights of produce, where the population variance is known to be $$16$$ (kg^2).

Sampling Distribution for Sample Proportions in a Survey

A survey indicates that 65% of viewers prefer streaming TV over cable. A random sample of 150 viewer

Sampling Distribution of Differences in Proportions

In a study of customer eating habits at two fast‐food restaurants, it was observed that at Restauran

Simulated Sampling Distribution for Rare Events

A rare genetic marker is present in only 1% of a large population. A random sample of 200 individual

Stock Returns Probability Calculation

Assume that annual stock returns are normally distributed with a population mean of 8% (0.08) and a

Technology Use and Academic Major

A survey was conducted to examine the relationship between academic major and technology usage frequ

Unbiased Estimators: Evaluating Sample Slope

In a study of the relationship between hours studied and exam scores, a simple linear regression is

Voting Behavior by Gender

A political study analyzed voting behavior based on gender. The table below displays the counts of m

Website Load Time Evaluation

A popular website has load times that are approximately normally distributed with a mean of 3.5 seco

Analysis of Emergency Room Wait Times Satisfaction

A hospital surveyed patients about their satisfaction with emergency room wait times. In a sample of

Assessing New Advertising Campaign Effectiveness

A company runs a new advertising campaign. Out of 400 customers, 160 made a purchase within 24 hours

Comprehensive Analysis of Confidence and Significance in Survey Data

A political researcher conducted a two-part survey to analyze voter opinions on a new policy. The fi

Customer Satisfaction Survey by Region

A retail company conducted a customer satisfaction survey in two regions, North and South. Responses

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

Effect of Sample Size on Margin of Error

A researcher is investigating the effect of sample size on the margin of error when estimating a pro

Effectiveness of a New Vaccine

A pharmaceutical company is testing a new vaccine. In a clinical trial, out of 1500 participants, 13

Ethnicity and University Major

A university survey collected data on student major (STEM vs. Humanities) and ethnicity (Underrepres

Evaluating Strike Support

A union conducted a survey among 125 members to decide on whether to support a strike. In the survey

Margin of Error Analysis in a Health Survey on Vaccination Acceptance

A health department surveys 800 random individuals about their willingness to receive a new vaccine;

Online Shopping Behavior

A survey of customers on an e-commerce website evaluated purchasing behavior across two age groups:

Research on Smoking Cessation Program

A study is conducted on a smoking cessation program to estimate the proportion of participants who s

Social Media Usage Among Age Groups

A survey on social media usage was conducted among two age groups. Among individuals under 30, 160 o

Survey on Remote Work Satisfaction

A technology firm conducted a survey on remote work satisfaction among its employees. Out of 400 res

Urban vs. Rural: Survey on Public Transportation Usage

A survey was conducted to compare the use of public transportation between urban and rural residents

Vaccine Acceptance Rates

Researchers want to compare vaccine acceptance between urban and rural populations. In an urban area

Voter Approval Poll Design

A polling organization samples voters to estimate the proportion of the electorate that approves of

Accident Frequency Comparison

An assembly plant records the number of accidents per month in two independent departments over 30 m

Advertising Spending and Sales Regression Analysis

A researcher investigates the relationship between advertising spending (in thousands of dollars) an

Air Quality Measurements: Urban vs. Rural

An environmental scientist is interested in comparing the air quality between an urban area and a ru

Career Development Program

A corporation has implemented a career development program and wishes to assess its impact on employ

Comparative Analysis of Lecture Techniques Using Paired Data

A study compares two lecture methods implemented on the same group of 30 students. The students take

Comparing Average Wait Times at Two Coffee Chains

A study is conducted to compare customer wait times at two coffee shop franchises. The following sum

Comparing Delivery Times

A logistics company is comparing two shipping methods to determine which is faster. For method A, a

Comparing Teaching Methods via Test Scores

A school is comparing two teaching methods. In a study, 30 students using Method A had an average te

Daily Steps: Wearable Device Analysis

A fitness tracker company wishes to estimate the average number of steps taken per day by its users.

Dosage Effect on Symptom Reduction

In a clinical trial investigating the effect of a drug, researchers examine the relationship between

Engine Emissions Compliance

An environmental agency is monitoring engine emissions to ensure compliance with regulations that re

Evaluating a Sleep Intervention

A fitness center implements a sleep intervention program aimed at increasing the average number of h

Exam Score Analysis with Unequal Sample Sizes

A researcher compares exam scores between two sections of a course. Section A (n = 18) has a mean sc

Experience and Salary Analysis

The scatterplot below represents data on employees' years of experience (x-axis) and their annual sa

Fertilizer Impact on Plant Growth

An agricultural researcher investigates whether a new fertilizer affects plant growth. Two independe

Fuel Efficiency Analysis

A study is conducted to assess the fuel efficiency (in miles per gallon) of a new model of cars. A r

Investigating Student Reaction Times

A psychologist studies the reaction times of 30 college students using a computerized test. The meas

Investigative Analysis of Customer Service Performance Metrics

A company collects data on customer service performance across two centers. For a focused study on c

Machine Downtime Analysis

A manufacturing plant monitors the daily downtime (in minutes) of a critical machine. Over 40 indepe

Manufacturing Process Adjustment

A process engineer is investigating whether an adjustment to a machine can reduce the mean productio

Medical Device Response Time Analysis

A study is carried out to evaluate the response time (in seconds) of a new medical device. A random

Power Analysis in a Drug Efficacy Study

A pharmaceutical company is testing a new drug intended to lower blood pressure. The test is a one-s

Precision in a Manufacturing Process

A company claims that the mean diameter of a manufactured part is $$10$$ mm. An independent quality

Public Transportation Use and Environmental Awareness

A survey examines whether public transportation usage is related to environmental concern. Participa

Quality Control: Machine Calibration

A factory employs a machine to produce metal rods. To check the machine’s calibration, two samples o

Randomized Field Experiment on Stress Reduction

A research team is interested in determining whether a mindfulness training program reduces stress l

Reaction Time Testing Under Caffeine Effects

A study examines the effect of caffeine on human reaction times. Two independent random samples of 2

Simulating Sampling Distribution of Daily Temperatures

A simulation study was conducted to generate the sampling distribution of the sample mean daily temp

Simulation of Sampling Distribution for Average Calorie Content in Energy Bars

A food quality control manager conducts a simulation study to evaluate the average calorie content o

Simulation of Sampling Distribution for Mean Rainfall Amounts

A meteorologist simulates the sampling distribution of the average daily rainfall (in inches) record

Simulation of Sampling Distribution for Mean Recovery Time

A hospital administrator runs a simulation study to assess the average recovery time (in days) after

Soil pH Variation

An agricultural experiment is conducted to assess whether a new fertilizer treatment helps bring soi

Student Participation in Extracurricular Activities

Researchers are studying the relationship between club membership and academic achievement in a samp

Study Hours and Test Scores Regression Analysis

The scatterplot below displays data on college students' study hours (x-axis) and their correspondin

Technology Adoption in Businesses

A market analysis explores the relationship between company size and the adoption of new technology.

Weekly Hours Worked and Earnings Analysis

The scatterplot below displays data relating weekly hours worked (x-axis) to weekly earnings in doll

Candy Color Distribution Goodness-of-Fit Test

A candy manufacturer claims that the distribution of candy colors in a bag is 30% red, 20% blue, 25%

Candy Color Distribution: Chi-Square Goodness-of-Fit Test

A candy manufacturer claims that the distribution of colors in a bag of candies is as follows: red 2

College Major vs Gender: Chi-Square Test for Independence

A college survey recorded the number of students by major (Science, Humanities, Business, Arts) and

Comparing Preferences for Social Media Platforms Across Age Groups

A survey examines if social media platform preference is associated with age group. The data collect

Consumer Preference for Advertisement Types

A company believes that consumer preference for advertisement type follows the distribution: Online

Customer Satisfaction Across Store Branches: Chi-Square Test for Homogeneity

A retail chain surveys customer satisfaction across three store branches. Customers are classified a

Dice Fairness Goodness-of-Fit Test

A game designer claims that a six-sided die is fair, such that each face appears with probability $$

Diet Preference Among Athletes

In a study, three groups of athletes (Football, Basketball, Soccer) were surveyed regarding their di

Dietary Preferences Among Age Groups: Chi-Square Test for Independence

Nutritionists surveyed 300 individuals to examine if dietary preference (Vegetarian, Non-Vegetarian)

Drug Side Effects Analysis: Chi-Square Test for Independence

In a controlled clinical trial, researchers are investigating whether the frequency of certain side

Effect of Marketing Campaign on Brand Awareness

A company wishes to determine if exposure to its marketing campaign is associated with brand awarene

FRQ 19: Comparing Library Usage Patterns Among Departments

A university library collected data on usage frequency categories (Frequent, Occasional, Rare) from

Genetic Ratios in Plant Breeding – Chi-Square Goodness-of-Fit

In a plant breeding experiment, a dominant-recessive trait is expected to follow a 3:1 phenotypic ra

Investigative Analysis: Public Health Awareness Survey

A public health department conducts a multi-stage survey to assess health awareness among residents

Learning Style and Major Association Independence Test

A college survey of 300 students categorized them by their preferred learning style (Visual, Auditor

Music Genre Preferences Across Cities – Chi-Square Test for Homogeneity

A market research firm surveyed residents in four different cities (City A, City B, City C, City D)

Pet Ownership and Residence Type Independence Test

A city survey collected data on pet ownership (Owning a pet, Not owning a pet) and type of residence

Political Party and Environmental Concern

A survey studies the relationship between political party affiliation (Democratic, Republican, Indep

Population Distribution: Rural, Suburban, and Urban

A demographer expects that the percentages of households in a country living in Rural, Suburban, and

Preferred Study Methods: Homogeneity Test Across Colleges

Three colleges (X, Y, Z) surveyed students on their preferred study method: Group Study, Self Study,

Product Defect Rates – Chi-Square Goodness-of-Fit

A quality control engineer hypothesizes that defects in a product occur with equal probability among

Product Preference Independence Test by Gender

A survey of 200 participants gathered data on product preference among four options (Product A, B, C

Simulated Data: Random Number Generator Uniformity Test

A random number generator produced 1000 numbers that were binned into 10 equal intervals. The observ

Smartphone Brand Preference

A market research firm expects that smartphone brand preferences will follow the proportions: Brand

Species Distribution in a Wildlife Reserve

In a wildlife reserve, the theoretical model predicts that the species distribution should be: Mamma

Student Extracurricular Activities: Chi-Square Goodness-of-Fit

A high school believes that student interest in extracurricular activities (Sports, Music, Drama, Cl

Survey Response Distribution Goodness-of-Fit Test

A survey on public opinion regarding a new policy asks respondents to choose among Agree, Neutral, a

Voter Opinion and Cable News: Chi-Square Test for Independence

A survey of 500 voters was conducted to investigate the relationship between political party affilia

Voting Methods: Chi-Square Goodness-of-Fit

In a local election, voters could choose from three voting methods: In-person, Mail-in, and Online.

Advertising Budget and Revenue

A study on 25 companies examines the relationship between advertising budget (x, in thousands of dol

Advertising Budget and Sales Revenue

A company collected data on weekly advertising expenditure ($$x$$, in thousands of dollars) and corr

Advertising Expenditure vs Sales

A company investigated the relationship between the amount spent on advertising (in thousands of dol

Agricultural Study: Fertilizer and Crop Yield

In an agricultural study involving 52 plots, researchers investigated the effect of fertilizer usage

Agricultural Yield and Fertilizer Simulation

An agricultural scientist is examining the relationship between the amount of fertilizer used (in po

Biomarker Levels and Disease Severity Simulation

A biomedical study examines the relationship between blood biomarker levels (in mg/dL) and disease s

Car Fuel Efficiency and Car Weight Regression Analysis

An automotive engineer analyzes the relationship between a car's weight (in kg) and its fuel efficie

Daily Steps vs Calorie Burn

A fitness app developer examined the relationship between the number of daily steps and calorie burn

Elevation and Atmospheric Pressure

Atmospheric scientists study the relationship between elevation ($$x$$, in meters) and atmospheric p

Employee Experience and Salary

A human resources study examines the relationship between years of work experience ($$x$$) and annua

Energy Consumption and Temperature: Simulation Study

A data analyst is investigating the relationship between ambient temperature (in $$^\circ C$$) and h

Exercise Duration and Weight Loss

A fitness study explores the relationship between exercise duration (in minutes) and weight loss (in

Fish Population and Pollution Levels

Biologists are studying whether increased pollution levels (x, in parts per million) are associated

House Prices and Square Footage

A real estate study uses the square footage of houses (x, in square feet) to predict their prices (y

Ice Cream Sales vs Temperature

A local ice cream shop recorded daily temperature (in $$^\circ F$$) and sales revenue (in dollars) o

Impact of Workout Hours on Body Fat Percentage

A fitness study collected data on the number of hours individuals work out per week (x) and their bo

Industrial Emissions and Air Quality

A governmental agency is evaluating the impact of industrial emissions (x, in tons per day) on local

Multiple Regression: Interpreting Slope in Presence of Collinearity

In a study using multiple regression to predict housing prices, several predictors (e.g., square foo

Physical Activity and Weight Loss: Simulation Analysis

A researcher is studying the effect of weekly physical activity (in hours) on weight loss (in kg) us

Plant Growth and Fertilizer Amount

In an agricultural experiment, a researcher measured plant height (y, in cm) as a function of fertil

Practice Time and Music Performance Skill

A study investigates the effect of weekly practice hours ($$x$$) on a music performance skill score

Reaction Rate in Chemistry: Temperature and Reaction Time

An experiment investigates the effect of temperature (x, in °C) on reaction time (y, in seconds). Da

Replicating Slope T-Test Using Summary Statistics

A researcher reports a sample slope of 2.5 with a standard error of 0.5 based on 12 observations. An

Sleep Hours and Cognitive Performance

A study examines the effect of sleep hours (x) on cognitive performance (y, measured as a test score

Social Media Influence on Product Sales Simulation

A business analyst wants to understand the effect of time spent on social media advertising (in hour

Speed and Fuel Efficiency

A study examines the relationship between vehicle speed ($$x$$, in mph) and fuel efficiency ($$y$$,

Student Performance and Attendance

A school administrator wants to understand the relationship between class attendance and test scores

Study Hours and SAT Scores: Private vs Public

A researcher studied the relationship between study hours (x) and SAT scores (y) among students from