AP Statistics FRQ Room

Advertising Campaigns and New Customer Sign-ups

A company ran two advertising campaigns to increase new customer sign-ups. In Campaign 1, there were

College Graduation Rate Analysis

A college claims its graduation rate is 85%. In a survey of 200 students, 162 of them graduated with

Comparing Pass Rates for Two Classes

In a high school, two math classes took the same standardized test. In Class 1, 28 out of 35 student

Constructing a Frequency Histogram from Commute Times

A study recorded the commute times (in minutes) for 20 individuals. The raw data are: $$\{12, 15, 1

Consumer Smartphone Preferences Analysis

A survey was conducted at a shopping mall where 300 shoppers were asked about their preferred smartp

Cumulative Frequency Analysis of Age Distribution

A study compares the age distributions of two different years using cumulative frequency plots. In Y

Dotplot Representation of Home Run Distances

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

Effects of Linear Transformation on Data

Let a data set $$X$$ have a mean of $$\mu$$ and a standard deviation of $$\sigma$$. Suppose we defin

Effects of Sample Size on the Sampling Distribution in Temperature Data

A meteorologist is studying daily high temperatures in a city over the summer. The temperatures are

Employee Benefits Satisfaction Interval

A company conducted a survey on employee satisfaction with benefits. Out of a sample of 120 employee

Employee Salary Adjustments

A company’s six employee salaries (in dollars) are as follows: {3000, 7000, 15000, 22000, 23000, 380

Employee Salary Adjustments

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

Favorite School Lunch Choices

A survey was administered to 500 students about their favorite school lunch option. The partial data

Home Run Distances Analysis

Consider the following set of home run distances (in feet) measured at 13 ballparks: $$\{387, 400,

Home Run Distances: Mean, Median, and Outlier Impact

A dataset of home run distances (in feet) recorded in 13 ballparks is given as follows: {387, 400, 4

Investigative Task: Public Park Usage Study

A city park department seeks to understand how weather conditions affect park attendance. They plan

NBA Team Wins: Distribution Assessment

The numbers of wins for NBA teams in two conferences are summarized using comparative data displays.

New York City Taxi Mileage Distribution

Taxicabs in New York City are driven an average of 75,000 miles per year with a standard deviation o

Remote Learning Preference in High Schools

Two high schools surveyed their students regarding their preference for remote learning. In School A

Restaurant Wait Time Analysis

A consumer group claims that a certain fast-food restaurant’s average wait time is 4 minutes. They c

Simulation of Sampling Distribution of a Proportion in a Medical Recovery Study

In a clinical trial, suppose the true proportion of patients who recover from a treatment is 0.80. A

Student Test Scores Improvement

A teacher implemented a new teaching method and collected exam scores from 35 students. The sample d

Survey on Favorite Ice Cream Flavors

A survey asked 200 respondents about their favorite ice cream flavor. The collected data are summari

Survey Response Methods Comparison

A survey was administered using two methods: telephone and online. In the telephone survey, 115 out

University Course Selection by Gender

A university survey of 300 students recorded their course selection (STEM or Humanities) and gender

Assessing the Sampling Distribution of Predicted Values in Linear Regression via Simulation

In a study examining the relationship between advertising expenditure (x) and sales (y), a simulatio

College Major by Gender

A study was conducted at a college to examine the relationship between major category and gender. St

Contingency Table Analysis: Cuteness Factor Study

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

Customer Satisfaction: Online vs In-store Shopping

A retail company surveyed its customers about their satisfaction with online versus in-store shoppin

Dosage and Blood Pressure Reduction

In a clinical trial with 25 patients, the relationship between drug dosage (in mg) and reduction in

Elderly Health Program Evaluation

An evaluation was carried out to assess whether participation in a health program by elderly individ

Employment Rates of College Graduates

A survey was conducted to compare the employment outcomes of graduates from two colleges. College X

Exploring Temperature and Ice Cream Sales

A study was conducted to explore the relationship between daily temperature (in °F) and ice cream sa

Food Safety Inspections in Restaurants

In a restaurant chain, historical data show that 10% of health inspections result in a violation. In

Green Energy Adoption and Energy Savings

Data from 35 households were analyzed to study the relationship between the percentage of energy fro

Housing Prices and Home Size

A study of 40 houses produced the regression equation $$\hat{y}=50+0.15x$$ predicting house price (i

Housing Renovation Impact on Property Values

A real estate researcher is investigating whether the cost of home renovations (x, in thousands of d

Impact of Study Methods on Test Performance

A university is interested in determining the effect of different study methods on students' perform

Influential Points and Leverage in Salary vs. Experience

A human resources department collected data on 20 employees, recording their years of experience (X)

Internet Usage and Credit Card Fraud

A cybersecurity study examined the relationship between frequency of internet usage and whether indi

Marketing Survey: Advertising Budget vs. New Customers

A marketing survey collected data on weekly advertising budget (x, in thousands of dollars) and the

Online Learning Preferences

A survey was conducted among 200 students to determine their preferences for online learning. Studen

Promotion Program Success Comparison

A company implemented two distinct promotional programs to boost sales. In Program 1, 92 out of 150

Proof that the Mean of Residuals is Zero

Show mathematically that for a least squares regression model, the mean of the residuals is always z

Restaurant Tip Analysis

In a study of restaurant bills, data were collected on the total bill amount (in dollars) and the ti

Simulation Comparison of Unstandardized vs. Standardized Regression Coefficients

A data analyst performs a simulation study to compare the sampling distributions of unstandardized a

Social Media Activity and Face-to-Face Interactions

In a survey of 40 individuals, data were collected on the number of social media posts per week (x)

Specialty Coffee Orders at a Coffee Shop

At a coffee shop, 25% of customers order a specialty coffee. In a random sample of $$60$$ customers,

Urban Noise and Sleep Quality Study

A study investigated the impact of urban noise level (measured in decibels, x) on individuals' self‐

Academic Performance: Hours Studied and Test Scores

In a high school, a teacher investigates the relationship between the number of hours students study

Analysis of Recycling Behavior

A survey was conducted to study recycling habits among individuals with different education levels.

Assessing Sampling Techniques in Market Research for a New Product

A company plans to gauge consumer preferences for a new product by sampling shoppers at a busy mall

Cluster Sampling in Educational Research

A school district administrator wants to assess students' attitudes toward a new curriculum. To redu

Comparing Beverage Effects on Pulse Rates

Researchers conduct an experiment to compare the effects of coffee, caffeinated cola, and herbal tea

Effectiveness of Stress Reduction Methods: Yoga vs. Meditation

A wellness center studied the effectiveness of yoga and meditation on reducing stress. In the yoga g

Efficacy of a Mobile App for Tracking Physical Activity

A study compared the effectiveness of a mobile app in helping users meet their daily step goals. In

Film Ratings Analysis

A movie review aggregator collects ratings on a scale from 1 to 10 from a simple random sample of 80

Flu Vaccination Campaign and Illness Spread

A hospital is reviewing its flu vaccination campaign by comparing the incidence of flu among vaccina

Investigating Data Variability in Statewide Math Test Scores

A state education board uses multiple samples to estimate average math test scores across high schoo

Manufacturing Processes and Product Lifespan

A manufacturing company is testing whether a new production process can increase the lifespan of its

Monte Carlo Simulation and the CLT

A researcher conducts a Monte Carlo simulation by drawing 1,000 random samples, each of size 30, fro

Observational Study on Dietary Habits and Exam Performance

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

Physical Activity and Cognitive Function in Older Adults

Researchers are investigating whether increased physical activity is associated with better cognitiv

Placebo-Controlled Experiment in Nutritional Supplements

Researchers are studying the effect of a new nutritional supplement on muscle recovery times. Partic

Replication in Experimental Designs: Water Purification Study

Researchers are testing various water purification techniques in an experimental study. Replication

Retail Customer Purchase Binomial Model

A retailer estimates that the probability of a customer making a purchase during a visit is 10%. On

Sampling Variability in Teacher Performance Evaluations

A school district collects teacher performance evaluations through student surveys. The administrati

Simulating the Effect of Sample Size on Standard Errors

A study is performed using simulation to assess how sample size affects the standard error of the sa

Social Media Use and Academic Performance

A study is conducted to explore the relationship between daily hours spent on social media (x) and a

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

Systematic Sampling in a Traffic Accident Study

A city transportation department wants to assess the frequency of traffic accidents at intersections

Using Random Digit Tables in Clinical Studies

In designing a clinical study, researchers decide to use a random digit table to select a simple ran

Apartment Rental Prices Estimation

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

City Traffic Speed Analysis

The city transportation department collected data on the speeds of vehicles on a major highway. A ra

Coffee Shop Latte Prices

A national coffee shop chain wants to estimate the average price of lattes across its stores. A rand

Coin Flip Game Strategies

In a game show, contestants face two different coin flip challenges. In Challenge A, you win if the

Comparing Patient Wait Times at Two Clinics

Two clinics recorded patient wait times. Clinic 1 (n = 40) had an average wait time of 25 minutes wi

Cumulative Distribution Function Analysis for Daily Customers

A small store tracks its daily customer counts and summarizes the data with the following cumulative

Effects of Outliers on Sampling Distributions

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

Fuel Efficiency Comparison between Two Vehicle Models

An automotive study compared the fuel efficiency of two car models. Model X was tested on 30 cars, y

Genetics: Inheritance Probabilities

In a certain plant species, each seed has a 75% probability of inheriting a dominant allele, indepen

Impact of Study Aid on Exam Pass Rates

A school collected data on standardized exam pass rates. Among students who used a study aid, 85 out

Insurance Sales Analysis

An insurance salesperson's daily sales for auto and home insurance are represented by two independen

Library Book Borrowing Times

A public library claims that the average time a book is borrowed is 3 weeks. A random sample of 40 b

Lottery Expected Value

A charity lottery sells 5000 tickets at $$\$2$$ each. One winning ticket receives a prize of $$\$500

Medical Treatment Recovery Rates Comparison

A clinical trial compared two treatments for a particular medical condition. Treatment A was adminis

Public Opinion Survey on Local Issues

A political analyst is conducting a survey to gauge public opinion on various local government polic

Quality Control Binomial Process

A manufacturing process produces items such that each item has a $$5\%$$ chance of being defective.

Random Variable Transformation in a Carnival Game

A carnival game offers three possible payouts: $$\$2$$ with probability 0.5, $$\$5$$ with probabilit

Sales Calls Geometric Distribution

A salesperson makes calls until she gets her first sale. The probability of getting a sale on any gi

Sampling Distribution of the Sample Range

Consider a simulation where samples are drawn from a uniform distribution on the interval $$[0,1]$$.

Suit Name Letter Count

A card is drawn from a standard 52-card deck. Let the random variable $$X$$ be the number of letters

Tip Amounts from Different Meal Services

At a restaurant, a waiter receives tips from two independent services. For lunch, the tip is modeled

University Admissions Multistage Process

A university's admissions process consists of two independent stages. A student first undergoes a sc

Website Conversion Rates: A/B Testing

An online retailer is testing two different webpage designs. Landing Page A received 120 conversions

Advanced Experimental Design in Teaching Methods

A researcher is investigating the effectiveness of two teaching methods by comparing student test sc

Analyzing Daily Coffee Sales Sampling Distribution

A local coffee shop claims its daily sales (in dollars) are normally distributed with a mean of $$\m

Analyzing Differences in Means Between Two Machines

Two machines produce metal rods. Machine A produces rods with a mean length of $$20$$ cm and a stand

Assessing Bias in Weight Measurements

A shipping company is evaluating three different types of scales (A, B, and C) for measuring package

Caffeine Content Analysis

An energy drink has a caffeine content that is normally distributed with mean $$\mu = 150$$ mg and s

Central Limit Theorem in Customer Service Times

In a call center, individual call durations are skewed with an average of $$\mu = 5$$ minutes and a

Coffee Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Sampling Distributions from Two Populations

Population A has a mean of 100 with a standard deviation of 15, while Population B has a mean of 105

Comparing Variability in Two Measurement Methods

Two independent methods are used to measure the voltage of a battery. Method 1 produces individual m

Consumer Reviews: Variability Analysis

A popular online product has consumer ratings on a 1-to-5 star scale. In a random sample of 100 revi

Customer Complaints by Service Type

A telecommunications company recorded customer complaints for two types of services: Phone Service a

Differences in Daily Step Count due to Wellness Program

A company introduced a wellness program and wants to assess its impact on daily step counts among it

Effect of Sample Size on Variability of Estimator

A researcher collects repeated samples from a population with a known mean of $$\mu = 100$$ and stan

Energy Drink Caffeine Analysis

An energy drink contains on average $$200$$ mg of caffeine with a standard deviation of $$10$$ mg. A

Environmental Concerns by Community Type

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

Environmental Study: Tree Heights

A biologist is studying tree heights in a forest. Although individual tree heights are not normally

Estimator Comparison for Population Mean

Consider two estimators for a population mean: the sample mean $$\bar{x}$$ and a 10% trimmed mean (w

Estimator Evaluation in Baseball Manufacturing

In a quality control study for manufacturing professional baseballs (true mean weight = $$146$$ gram

Estimator Evaluation in Quality Control

A manufacturing process is designed to produce products weighing 500 grams. Four estimators (E1, E2,

High Math Anxiety and Brain Activity

It is estimated that $$80\%$$ of individuals with high math anxiety exhibit brain activity indicatin

LED Lightbulb Lifespan Probability Analysis

A manufacturer produces LED lightbulbs whose lifespans are normally distributed with a mean of $$\mu

Lightbulb Lifespan Probabilities

A certain brand of lightbulbs has a lifespan that is normally distributed with mean $$\mu = 1500$$ h

Manufacturing Process Consistency and Variability

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

Math Anxiety Brain Activity Proportions

It is estimated that $$80\%$$ of individuals with high math anxiety exhibit brain activity similar t

New Drug Effect on Blood Pressure Reduction

A clinical trial is evaluating a new drug that is believed to reduce blood pressure. Historically, t

Political Opinion Poll on Policy Support

A political opinion poll was conducted to determine the relationship between political affiliation a

Regression Analysis and Inference in a Health Study

A health study investigates the relationship between Body Mass Index (BMI) and systolic blood pressu

Sampling Distribution of Differences in Proportions

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

Simulation of Dream Recall Sampling Distribution

A study records the number of dreams high school students remember each night. The population median

Simulation Study of Income Medians

A researcher studies household incomes, which are heavily right-skewed. The population has a median

Social Media Usage by Age Group

A survey examined the social media usage intensity among different age groups. The table below categ

Sports Performance Data Analysis - Batting Averages

In a baseball league, the average batting average is 0.280 with a standard deviation of 0.030. A coa

Student Extra-Curricular Participation

A school conducted a survey to understand students' involvement in extracurricular clubs. The table

Student Performance and Study Techniques

A study compared two study methods: using flashcards versus summarization. In the flashcards group (

Survey on Learning App Preference

In a high school, it is believed that $$65\%$$ of students prefer using a new learning app. A random

Analysis of Emergency Room Wait Times Satisfaction

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

Analyzing Election Poll Data: Estimating the Margin of Error

An election poll of 1000 voters produced a sample proportion of $$\hat{p}=0.48$$ for Candidate A. As

Assessing New Advertising Campaign Effectiveness

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

Community Recycling Program Study

A city implements a program aimed at increasing household recycling rates. Two neighborhoods with si

Comparing Participation Rates in Exercise Programs Across Cities

Two cities conducted surveys about participation in exercise programs. City X had 250 participants o

Confidence Interval for Proportion in Market Research

A market research firm surveys 500 consumers and finds that 265 like a new product.

Consumer Preference: Hypothesis Testing for a Single Proportion

A company claims that at least 40% of consumers prefer its new product. In a sample of 250 consumers

Customer Preference Difference Between Cities

A regional chain surveys customers in two cities regarding their preference for a new product. In Ci

Determining Required Sample Size for Test Power

A public health researcher is testing the claim that the proportion of adults who smoke is less than

Environmental Study: Testing Proportion Exceeding Safety Threshold

A study of water quality in a river found that 18 out of 90 samples exceeded the safety threshold fo

Estimating Social Media Usage Proportions

A research study surveyed 750 social media users to estimate the proportion who use a specific app d

Ethnicity and University Major

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

Government Policy Approval Confidence Interval

A polling organization surveyed 800 voters to measure the approval of a recent government policy. Am

Health Study: Smoking Prevalence Comparison

A health study compared the smoking prevalence between two cities. In City A, a sample of 500 respon

Hospital Infection Rates: Hypothesis Testing

A hospital claims that its post-surgery infection rate is 2%. In a sample of 500 patients, 18 develo

Hypothesis Testing and Errors: Sports Performance

A coach claims that at least 70% of his players hit a home run. In a game, 50 players are observed a

Impact of New Educational Program

A school district implemented a new teaching method aimed at improving student performance. In a stu

Impact of Training Program on Certification Rates

A company implemented a training program to improve certification rates among its employees. In a ra

Medical Treatment Outcomes

A clinical trial compares the outcome of a new drug with a placebo. Patients were classified as eith

New App Adoption Rate Confidence Interval

A tech company is assessing the adoption rate of its new mobile application. A random sample of 500

One-Sided Election Polling Analysis

In a survey of 600 likely voters, 330 support a particular candidate. The candidate’s campaign claim

Online Education Satisfaction

A study comparing satisfaction with education methods surveyed two groups. One group of online stude

Online Shopping Proportion Analysis

A market research firm surveyed 600 consumers to determine whether they prefer online shopping over

Physical Activity App Study

A startup company developed a new mobile application aimed at encouraging physical activity. Users a

Political Opinion Poll Analysis

A political poll was conducted to assess support for a proposed tax bill. In a simple random sample

Recreational Activities and Injury Rates

A health study compared injury rates for participants in contact sports versus non-contact sports. I

Service Reliability Study Analysis

In a service reliability study, a small sample of 50 customer interactions produced 38 successful ou

STEM Club Gender Representation Study

A high school is investigating the proportion of female members participating in its STEM clubs. Par

Study on Diet Preference Differences

A research study examines the diet preferences of individuals choosing between Diet A and Diet B. Th

Test of a Hypothesis on Voter Turnout

A political analyst claims that at least 60% of registered voters participate in elections. A sample

Urban vs Rural Voter Support Analysis

A political poll collected data from two independent groups: urban voters and rural voters. In the u

Voter Turnout Behavior Survey

A political organization implements a get-out-the-vote campaign in several precincts and wishes to d

Website A/B Testing

An online retailer is testing two versions of its webpage (Version A and Version B) to determine whi

Caffeine Consumption and Reaction Times

A study aims to determine whether the consumption of caffeine affects reaction times. Two independen

Comparative Analysis of Daily Sales at Two Branches

Two branches of a store report their average daily sales. Branch A has a sample of $$n=30$$ with a m

Comparing 3-Point Percentage Rates

A sports analyst wants to compare the true 3-point shooting percentages of two basketball players. I

Comparing New Drug Efficacy

A pharmaceutical study compares two medications for lowering blood pressure. Group 1 (Drug A) consis

Comparing Two Diets

A nutritionist compares the effects of two diets on weight loss. In a study, Diet 1 (n = 30) results

Comparison of Waiting Times: Urban vs. Rural Hospitals

A health researcher compares patient waiting times in emergency rooms between urban and rural hospit

Daily Sales Confidence Interval

A store recorded its daily sales for 30 days, and the sample data yielded a mean of 200 units sold p

Diet Choice and Energy Levels

A nutritionist investigates whether there is an association between diet type (Vegetarian vs. Omnivo

Employee Training and Productivity Outcome

A company examines whether the type of training (Online vs. In-person) affects employee productivity

Enzyme Activity Confidence Interval

A laboratory measures enzyme activity in 12 samples. The sample mean enzyme activity is 7.5 units wi

Fuel Consumption and Distance Traveled Analysis

The scatterplot below displays data on the gallons of fuel used (x-axis) and the corresponding dista

Gas Mileage Analysis: Confidence Interval Assessment

A manufacturer tests 12 cars of a new model. The sample yields a mean gas mileage of $$28.5$$ miles

Impact of a Diet Program on Weight Loss

A weight loss study measures the weight of 20 participants before and after a 6‐week diet program. T

Impact of a Study Program on Exam Performance

A school introduces an intensive study program and measures students' exam scores before and after i

Impact of Advertising on Product Awareness

A marketing team wants to analyze the effect of advertising on product awareness. Consumers are cate

Life Span Analysis of Light Bulbs

A manufacturer claims that its light bulbs have a long lifespan. In a quality test of 15 randomly se

Lifespan of New Light Bulbs

A company tests the lifespan of a new type of light bulb. A random sample of 18 bulbs shows a mean l

Machine Calibration Paired Data

A manufacturer tests the effect of a maintenance update on machine calibration. Fifteen machines are

Pre- and Post-Intervention Test Score Analysis

An educational researcher wants to evaluate the effect of a new study program on student performance

Rainfall Measurement Study

A meteorologist records daily rainfall (in mm) over 20 days in a region. The sample has a mean of 12

Reaction Time Hypothesis Test

A psychologist wishes to test a manufacturer's claim that the average driver reaction time is \(0.8\

Recovery Rates in Two Hospitals

A study compares recovery rates between two hospitals. Patients are classified as 'Recovered' or 'No

Simulation of Sampling Distribution in Environmental Air Quality

An environmental scientist conducts a simulation study to analyze the sampling distribution of the a

Simulation of Sampling Distribution with Measurement Error

A lab is troubleshooting a sensor that measures the weight of produced components. A simulation is c

Sleep Duration and Reaction Time Analysis

The scatterplot below shows data on hours of sleep (x-axis) and reaction time in seconds (y-axis) fr

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

A teacher implements a new study method to improve student performance. Eight students are tested be

Temperature and Ice Cream Sales Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and the number of ice cream con

Test Scores in a New Curriculum

A school implements a new curriculum and collects standardized test scores from a random sample of 2

Bacteria Types in Environmental Sampling: Goodness-of-Fit Test

An environmental scientist collects 180 bacterial samples from a river and categorizes them into fou

Branch Service Quality

A bank is comparing customer satisfaction across its three branches. Each branch serviced 100 custom

Clinical Trial: Treatment Effects on Recovery Rates

In a clinical trial, patients are randomly assigned to one of three treatment strategies (Treatment

Clothing Preference and Gender: Test for Independence

A clothing store surveyed customers to see if there is an association between gender (male, female)

Coffee Preference in College

Three colleges conducted surveys of 150 students each to determine their preferred type of coffee: E

Customer Service Feedback in Retail Stores: Homogeneity Test

A retail chain surveys customer feedback from three stores. Feedback is classified as Positive, Neut

Effectiveness of a New Training Program across Branches

A company implements a new training program in three of its branches. After the program, employees a

Effectiveness of Advertisement Types

A study assesses whether the type of advertisement affects perceived effectiveness. Three ad types a

Examining Political Ideology: Chi-Square Test for Homogeneity

A political scientist collected data on ideological self-identification (Liberal, Moderate, Conserva

Goodness-of-Fit for Beverage Preferences

A local cafe expects customer beverage preferences to follow the distribution: Iced Coffee (40%), Ho

Goodness-of-Fit Test for Web Traffic Sources

A website manager expects that web traffic comes from four sources with the following proportions: D

Independence Test: Health Food Consumption vs. Age Group

A study collected data on whether individuals regularly consume organic foods (Yes/No) across three

Insurance Claim Types: Independence Test Across Age Groups

A study examines whether the type of insurance claim (Auto, Home, Health) is associated with age gro

Library Membership and Age

A library survey examines whether there is an association between age group and type of membership (

Medal Distribution across Training Groups Homogeneity Test

In a national sports event, athletes from three training groups (Group A, Group B, Group C) competed

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)

Online Shopping Day Preferences: Chi-Square Goodness-of-Fit

A retailer surveys 150 online shoppers to determine which day of the week (Monday through Friday) th

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 Polling: Party Affiliation and Issue Stance

A national poll cross-classifies respondents by party affiliation (Democrat, Republican, Independent

Preferred Study Methods: Homogeneity Test Across Colleges

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

Product Packaging Preference Across Regions

A company wants to verify if the color preference for product packaging is consistent across three d

Shopping Preferences: Homogeneity Test Across Regions

A retail chain surveyed customers in four regions on their preferred shopping mode: In-store or Onli

Social Media Usage Among Age Groups: Independence Test

A survey of 250 social media users collected data on their primary platform (Facebook, Instagram, Tw

Sports Preferences by Gender: Chi-Square Test for Independence

A survey of 300 students recorded their preferred sport (Basketball, Soccer, Tennis) and their gende

Student Enrollment by Gender and Major: Chi-Square Test for Independence

A university is investigating if student major (STEM, Arts, Business) is independent of gender (Male

Survey on Preferred Modes of Transportation

A city survey investigates residents’ preferred modes of transportation. The city’s transportation m

Transportation Mode Among City Residents

A city survey examines the relationship between type of residence (Urban vs. Suburban) and preferred

Travel Mode and Environmental Concern – Chi-Square Test for Independence

A survey of 250 commuters collected data on their primary travel mode (Car, Public Transit, Bike) an

Voter Registration Distribution

A state expects voter registration to follow the proportions: Democratic 25%, Republican 35%, and In

Voter Turnout by Age Group: Test for Independence

A survey reports voter turnout among four age groups: 18-29, 30-44, 45-64, and 65+. The two variable

Advertising Expenditure vs Sales

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

Advertising Spend and Website Traffic

A company analyzed how its weekly advertising spend (in thousands of dollars) influences website tra

Bicycle Speed vs Oxygen Consumption

A sports scientist is studying how bicycle speed (in mph) affects oxygen consumption (in ml/min) for

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

Coffee Consumption and Alertness

A study examines the relationship between cups of coffee consumed per day (x) and a measured alertne

Consumer Spending and Income Levels

An economist analyzed data from 60 households to study the relationship between household income (x,

Crop Yield and Fertilizer Application

An agronomist is examining how the amount of fertilizer applied (x, in kg) affects crop yield (y, in

Dosage-Response in Drug Trials Simulation

A clinical researcher investigates the effect of drug dosage (in mg) on patient response scores. To

Effect of Study Habits on Exam Scores

Researchers are studying whether the number of extra study sessions (x) is related to improvement in

Effect of Study Time on Test Scores

A teacher collects data on the number of hours studied (x) and exam scores (y) out of 100 for 25 stu

Electricity Usage and Temperature

An energy analyst examines how average daily temperature (x, in °F) affects household electricity us

Employee Salary and Years of Experience

A human resources analyst uses years of experience (x) to predict annual salary in thousands of doll

Energy Consumption and Temperature: Simulation Study

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

Environmental Pollution and Distance Simulation

An environmental scientist is investigating how the concentration of a pollutant (in ppm) changes wi

Exam Scores vs Hours Studied

A study collected data on the number of hours studied (x) and exam score (y) for 20 students. A scat

Internet Speed and Streaming Buffer Time

A technology company studies the relationship between home internet speed (x, in Mbps) and streaming

Machine Runtime and Maintenance Costs

An operations manager is investigating whether the total runtime of an industrial machine (in hours

Measurement Error Impact on Slope Estimation: Simulation Study

An industrial engineer investigates the relationship between machine speed (in rpm) and the number o

Online Course Hours and Final Grades

An educational researcher is modeling final course grades (y, in percentage) as a function of the nu

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

Practice Time and Music Performance Skill

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

Predicting Sales Based on Advertising Budget

A company wants to understand the relationship between its advertising spending (in thousands of dol

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

Robotics and Efficiency

A robotics company collects data from 15 production lines to examine the relationship between the nu

Study Time and Exam Scores

A study was conducted to examine the relationship between hours of study (x) and exam scores (y) for

Water pH and Aquatic Life Diversity

Environmental scientists are investigating the relationship between water pH (x) and aquatic life di