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

Almond Packet Weight Confidence Interval

A quality control team at an almond packaging company wants to estimate the mean weight of its packe

Analysis of Categorical Data from Elections

A recent survey sampled 1000 voters to determine their preferred candidate in a local election. The

Analyzing z-Scores from a Frequency Distribution

The following table displays z-scores along with their corresponding cumulative percentile rankings

Basketball Free Throw Percentage Confidence Interval

A basketball player takes 80 free throws and makes 60 of them. Answer the following parts:

Boxplot Comparison: Stock Price Fluctuations Over Years

A company's daily stock prices over five consecutive years are summarized in the following table: |

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

Charitable Donation Timing by Age Group

A charity collected data on donation timings (Morning, Afternoon, Evening) and donor age group (Youn

College Admissions Test Scores

Test scores for a college admissions exam are approximately normally distributed with a mean of $$50

Community Exercise Program and Blood Pressure Reduction

A public health study is conducted to evaluate the effectiveness of a community exercise program on

Daily Step Count Hypothesis Test

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

Effect of a Multiplicative Transformation on Distance Data

A group of athletes has their running distances (in kilometers) recorded as: {5, 6, 8, 7, 10, 9}. Th

Effect of Price Increase on Customer Participation

A grocery store wanted to see if a recent price increase on a popular product affected customer part

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

Employee Benefits Satisfaction Interval

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

Event Attendance by Invitation Type

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

Home Run Distance Analysis

A study measured the distances (in feet) of home runs at 13 ballparks using the following data set:

Hospital Wait Time

In an emergency room (ER), patient wait times in minutes are normally distributed with a mean of $$4

Impact of an Outlier on Summary Statistics

Consider the data set $$\{4, 5, 6, 7, 50\}$$. Answer the following:

Impact of Transformations on Data

Consider the following dataset representing test scores: {70, 80, 85, 90, 100}. Answer the followin

Interpreting a Dot Plot of Daily Coffee Consumption

A dot plot summarizes the number of cups of coffee consumed per day by individuals in a small office

Interpreting Boxplots for Salary Data

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

Leadership Training and Employee Satisfaction

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

Matching Data Sets and Estimating Percentiles

A cumulative frequency table for exam scores of 100 students is provided below: | Score | Cumulativ

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

Online Retail Customer Spending Analysis

An online retail store collects data on customer spending. In a sample of 60 customers, the mean spe

Parent Survey on School Length

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

Political Polling: Candidate Preference

In a political poll, two states were surveyed to determine the proportion of voters favoring Candida

Product Length Variability in Manufacturing

A manufacturing process produces items with lengths (in centimeters) distributed as shown in the fre

Salary Analysis: Effect of Raises on Mean Salary

A company has six employees whose current salaries are $$3000$$, $$7000$$, $$15000$$, $$22000$$, $$2

Sampling Distribution of the Median in a Skewed Production Process

A factory produces components whose lifespans (in hours) are right-skewed due to occasional defects.

Sports Participation and Club Membership

A college survey collected data on students' participation in sports (Yes, No) and their club member

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

Survey of Smartphone Usage Time

A survey of 500 students categorized their daily smartphone usage (in hours) with the following data

Voting Behavior by Education Level

A political survey collected data on voters' education level (High School, College, Graduate) and th

Weekly Exercise Sessions

Assume that on any given day, a person exercises for at least 30 minutes with a probability of $$0.4

Advertising Campaign and Sales Analysis

A company tracked the number of social media impressions (in thousands, x) and corresponding product

Call Center Quick Resolutions

At a call center, the probability that a call is resolved within 3 minutes is $$0.2$$. Let $$Y$$ rep

Coffee Shop Drink Preference

A survey at a coffee shop collected responses from 120 customers regarding two categorical variables

Comparing Regression Lines for Calorie Consumption in Two Groups

A study compares the relationship between body weight (x) and calorie burn (y) for two groups: men a

Consumer Beverage Preference Analysis

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

Correlation between Exercise and Weight Loss

A fitness center collects data on the number of hours clients exercise per week and the weight loss

Correlation vs. Causation Discussion

A study finds a high positive correlation between ice cream consumption and the number of drowning i

Customer Loyalty Program Analysis

A retail company collected data on the number of store visits (x) by loyalty card members and the po

Customer Service and Order Mode Inference

In a survey at a local restaurant, 70 customers ordered online and 30 ordered in-person. Among the o

Detecting Fraud in Insurance Claims

An insurance company estimates that 3% of claims are fraudulent. In a sample of $$150$$ claims, let

Effect of Advertisement Frequency on Brand Recognition

A marketing study was conducted to analyze the relationship between the number of advertisements see

Effectiveness of a New Curriculum

A school district implemented a new curriculum in some of its schools and maintained the traditional

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

Evaluating Public Health Data on Smoking and Lung Cancer

A study was conducted to investigate the association between smoking and lung cancer incidence among

Examining the Sampling Distribution of the Mean Difference in Two Groups via Simulation

A researcher collected test scores from two different classes with 30 students each. She wants to si

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

Inference on the Slope of Study Hours vs. Exam Score

A researcher studies the relationship between the number of hours students study (x) and their exam

Limitations of Simple Linear Regression

Discuss the limitations of using a bivariate (simple linear) regression model when other explanatory

Manufacturing Defects in Two Production Lines

A manufacturing company operates two production lines. A quality control inspection was performed on

Neighborhood Safety Survey

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

Predicting Fitness Improvement from Exercise Duration

A fitness study examined the relationship between the daily exercise duration (x, in minutes) and th

Restaurant Service and Tipping

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

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,

Startup Revenue Growth

A startup's monthly revenue (in thousands of dollars) is approximately normally distributed with a m

Temperature and Ice Cream Sales

An ice cream vendor records daily maximum temperatures (in degrees Fahrenheit) and the number of box

Workforce Diversity Study

A corporation conducted a study to analyze the distribution of employees across different job levels

Analyzing Student Study Habits

A high school conducted a study comparing student performance based on their method of studying. The

Bias in Random Digit Sampling

A researcher uses random digit dialing to contact households for a survey. However, certain demograp

Cluster Sampling in Educational Research

A researcher wants to study academic performance across a large school district. The district is div

Comparing Disease Incidence in Two Regions

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

Designing a Prospective Study for Teaching Methods

A school district wants to study the effect of a new teaching method on student performance on stand

Designing a Representative Student Survey

A university desires to survey its 10,000 students about campus dining experiences. To ensure repres

Designing a Stratified Random Sample for Student Opinions on Distance Learning

A researcher intends to survey high school students' opinions on the transition to distance learning

Differences in Data Collection Techniques: Face-to-Face vs. Online Surveys

A political research firm collects survey data about voter opinions through both face-to-face interv

Effect of Diet on Cholesterol Levels

A prospective observational study monitored 100 adults for 6 months. Two groups were observed: one f

Evaluating Bias in a Sampling Process: Voluntary Survey

A city council conducts a voluntary online survey regarding community safety. Out of 150 responses,

Evaluating Survey Question Wording Bias

Two versions of a survey question on school lunch satisfaction have been designed. Version A states:

Evaluating Survey Sampling Methods

A researcher conducts an online voluntary response survey to measure public opinion on a new policy.

Evaluating the Effect of Exercise on Blood Pressure Reduction

A study measured the reduction in blood pressure in two groups over a 6‐month period. Group 1 (Exerc

Firearm Safety Course Outcomes in Different Regions

A study examined the outcomes of a firearm safety course in two regions. In Region X, 160 out of 200

Impact of Sample Size on Confidence Interval Width

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

Impact of Sample Size on Variability

In a study investigating average daily water consumption, two different sample sizes are used: one s

Influence of Outliers on the Sampling Distribution of the Sample Median

In studies of household incomes, extreme high incomes (outliers) can heavily influence the sample me

Measurement Reliability in Climate Data Collection

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

Scatterplot Analysis and Regression Line Interpretation

A researcher investigates the relationship between the number of hours studied (x) and exam scores (

Social Media Usage among Teenagers

A survey of teenagers collected data on social media platform preferences (Instagram, Snapchat, TikT

Study Habits and GPA: A Regression Analysis

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

Systematic Sampling in a Voter Preference Survey

A polling organization is using systematic sampling to select registered voters from a telephone dir

Teaching Methods and Student Performance

A school wants to compare the effectiveness of two different teaching methods on student performance

Use of Public Transport vs. Car Ownership

A transportation study categorized individuals by region (Urban, Suburban, Rural) and their car owne

Using a Random Digit Table for Sampling

A school intends to randomly select 15 students from a list of 120 using a random digit table. Answe

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

Voting Patterns in a Retrospective Study

A retrospective study collected exit poll data to determine the level of support for Policy X among

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

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

Binomial Distribution in Lightbulb Defectiveness

In a quality control test, the probability that a lightbulb is defective is $$0.1$$. Answer the foll

Casino Free Chips: Pooling Strategies

At a casino, two individuals each draw a card from separate bags. Bag $$X$$ contains the numbers {$$

Charity Lottery Expected Value Calculation

A charity holds a lottery selling 10,000 tickets at $$1$$ each. One ticket wins a prize of $$7500$$.

Coffee Shop Latte Prices

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

Cumulative Probability Distribution in AP Exam Scores

The following table shows the distribution of scores on an AP exam: | Score | Frequency | |-------|

Customer Retention and Marketing Strategies

A company tested two marketing strategies to improve customer retention. Strategy 1 retained 240 out

Customer Satisfaction Survey on New Service Protocol

A company is testing a new customer service protocol to improve satisfaction. Customers are randomly

High School SAT Scores Analysis

A school district collected SAT scores from a random sample of 60 students. The sample mean is $$\ba

Impact of Sleep Duration on Reaction Time

A research lab is investigating how different amounts of sleep affect reaction times measured on a s

Lottery Ticket Expected Outcome

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

Machine Failures in a Factory: A Binomial Approach

In a factory setting, each machine fails with a probability of $$0.05$$ on a given day, independentl

Medical Screening Test Accuracy by Gender

A medical screening test was administered to 1000 individuals, 500 males and 500 females. The result

Monthly Supermarket Expenditures

A local supermarket chain wants to estimate the average monthly expenditure of its customers. A rand

Public Opinion Survey on Local Issues

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

Quality Control in Manufacturing

A factory produces widgets, each having an independent 5% chance of being defective. Quality control

Simulated Distribution of the Difference of Sample Means

In a simulation comparing two independent groups (for example, treatment and control), separate samp

Simulating Clinical Trial Successes

A new drug has a success probability of 0.65. In a clinical trial, 30 patients are treated independe

Sleep Duration and Reaction Time Regression Analysis

A study looks at how sleep duration (in hours) affects reaction time (in milliseconds) on a computer

Small Business Daily Revenue Analysis

A small business tracked its daily revenue over a period of 30 days. The sample mean daily revenue w

Student Study Hours and Exam Performance Regression Analysis

A researcher examines the relationship between the number of hours a student studies (x) and their e

Transforming Payouts in a Carnival Game

A carnival game pays out according to a random variable $$X$$ with outcomes: $10 (p = 0.4), $20 (p =

Transportation Delay Times

A city's bus service experiences delays (in minutes) according to the following distribution: | Del

Website Conversion Rates: A/B Testing

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

Analysis of Athletic Performance Improvements

A coach is comparing the performance improvements of athletes following two different training progr

Assessing Bias in Weight Measurements

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

Assessing Estimators for Baseball Weight

A manufacturer is evaluating five different estimators for the weight of professional baseballs. The

Central Limit Theorem in Quality Control

A flour packaging machine fills bags that are intended to weigh 50 pounds on average with a standard

Coffee Consumption and Alertness

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

College Major and Internship Experience

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

Comparing Average Temperatures in Two Cities

City A has an average temperature of 70°F with a standard deviation of 5°F based on a sample of 50 d

Comparing Class Test Scores

Two independent classes took a standardized test. Class X (with $$n=30$$) had a mean score of 78 wit

Comparing Pass Rates Between Two Schools

Two high schools are comparing their students' pass rates on a standardized test. School A had 200 s

Comparing Variability: Averages versus Individual Values

In environmental testing, individual measurements of a pollutant level exhibit high variability. A s

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

Diet Preferences and Exercise Habits

A health survey sought to determine if there is any association between an individual’s diet prefere

Difference in Proportions: Fast Food Restaurant Study

A study compares customer behavior at two fast-food restaurants. At the revamped restaurant, $$25\%$

Estimating Average Commute Time

A study suggests that the average commute time in a metropolitan area is $$\mu = 30$$ minutes with a

Evaluating Customer Satisfaction Proportions

A restaurant chain wants to compare customer satisfaction between two of its locations. At Restauran

Evaluating Estimators for Baseball Weight

A quality control department is evaluating five different statistical estimators to measure the weig

Evaluating Sample Proportions in a Survey

A campus dining satisfaction survey indicates that 70% of all students are satisfied with the dining

Evaluation of Estimators in Baseball Manufacturing

A sports equipment manufacturer is evaluating five different estimators (A, B, C, D, and E) used to

Hospital Emergency Room Waiting Times

The waiting times (in minutes) for patients in a busy hospital emergency room are approximately norm

One-Sample vs. Two-Sample Sampling Distributions

A study is conducted to assess the effectiveness of a new teaching method. Two groups of 40 students

Smartphone Battery Life Comparison

A technology review compared the battery life of two smartphone models. Model X was tested with 60 p

Student Performance and Study Techniques

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

Air Quality Health Survey Design

A public health department is conducting a survey to estimate the proportion of residents suffering

Analysis of Emergency Room Wait Times Satisfaction

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

Comparing Two Proportions: Online vs. In-Store Shopping Preferences

A researcher compares shopping preferences. In a sample of 300 online shoppers, 210 prefer online sh

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

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

Manufacturing Process Comparison

A company employs two manufacturing processes. In Process A, a sample of 500 items produced 450 defe

Medical Study: Prevalence of a Risk Factor

A public health survey was conducted to determine the prevalence of a certain risk factor. In a simp

Online Advertising Impact Study

An online retailer wishes to study whether exposure to a particular digital advertisement increases

Online Shopping Behavior

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

Physical Activity App Study

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

Product Return Rates by Category

A retail store analyzed product return rates for different categories. Products are classified into

Public Transit Usage

A city planning study compares the proportion of residents using public transit in two cities. City

Retail Coupon Usage Among Customers

Two retail outlets want to know if they differ in the rate of coupon usage among their customers. Ou

Student Housing and Meal Plan

A university surveyed students on their housing situation and meal plan status. Students are classif

Student Satisfaction in Two College Courses

A survey was conducted in two college courses to measure student satisfaction. In Course 1, 90 out o

Survey Analysis: Confidence Interval for College Students' Online Class Preference

A survey of college students was conducted to estimate the proportion of students who prefer online

University Enrollment Statistics

A university collected enrollment data to compare the study mode (Full-time vs. Part-time) of Domest

Vaccine Acceptance Rates

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

Accident Rates Comparison Between Departments

A study was conducted over 20 months in two departments of an assembly plant to compare accident rat

Battery Life Study

A battery manufacturer claims that the new battery model has an average lifespan of $$\mu$$ hours. A

Blood Pressure Reduction Confidence Interval

A clinical trial was conducted to test the effectiveness of a new medication on reducing blood press

Comparing Manufacturing Processes

A company uses two different processes to manufacture a particular part. Process X is evaluated on a

Comparing Two Diet Programs on Weight Loss

A nutritionist wants to compare two different diet programs to determine which one leads to greater

Comparing Two Methods of Estimating Reaction Time

A researcher is comparing two methods for measuring reaction time. Using Method 1 on a sample of 15

Customer Wait Time in Service

A supermarket manager records the wait times (in minutes) for customers at a checkout counter. In a

Effectiveness of Tutoring Program Investigation

A school district is interested in the effectiveness of a new tutoring program on improving student

Energy Consumption Analysis

An energy company is testing the claim that the average daily electricity consumption of households

Evaluating a Sleep Intervention

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

Impact of Advertising on Product Awareness

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

Impact of Variability on Confidence Intervals: A Simulation Study

A simulation study is conducted to explore how differences in sample variability affect the width of

Machine Cycle Time Analysis

A manufacturing plant produces a critical component that goes through an automated production proces

Manufacturing Measurement Variability

A quality control procedure involves monitoring the variability in a product's critical dimension us

Monthly Sales Performance Analysis

A retail store assesses the impact of a promotional campaign on monthly sales. The data collected co

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

Recovery Rates in Two Hospitals

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

Sample Size Effect on Component Length Confidence Interval

In a manufacturing process, the length of a component is measured. A sample of measurements yields a

Simulation of Sampling Distribution in a Clinical Trial

A medical researcher conducts a simulation to analyze the sampling distribution of the mean systolic

Simulation of the Sampling Distribution for Mean Internet Connection Speeds

An internet service provider uses a simulation to assess the sampling distribution of average speeds

Simulation of the Sampling Distribution for Mean Salary

A company's HR department conducts a simulation study to understand the sampling distribution of the

Analyzing Website Navigation: Chi-Square Test for Independence

A study examining whether the navigation path taken on a website is related to the type of device us

Animal Species Distribution in Habitats: Chi-Square Test

Researchers collected counts of three animal species (Deer, Rabbit, Fox) in two habitats. The counts

Candy Flavor Preferences: Goodness-of-Fit Test

A local candy shop claims that customer preferences for its four candy flavors (chocolate, strawberr

College Major vs Gender: Chi-Square Test for Independence

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

Consumer Brand Preference Homogeneity Test

A consumer survey was conducted comparing brand preference for three competing brands (Brand X, Bran

Consumer Preference for Advertisement Types

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

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 Preferences Among Teenagers: Goodness-of-Fit Test

A survey of 150 teenagers categorizes their diet preferences as Vegetarian, Vegan, Omnivore, and Pes

Effectiveness of Advertisement Types

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

Exercise Frequency and Music Preference – Chi-Square Test for Independence

A gym surveyed 150 members to study the relationship between exercise frequency (categorized as Low,

Extracurricular Participation and Academic Performance Independence Test

A survey of high school students collected data on extracurricular activity participation (Yes, No)

Favorite Ice Cream Flavor Goodness-of-Fit Test

A market survey hypothesizes that the favorite ice cream flavors are distributed as: Chocolate 40%,

FRQ 11: Distribution of Emergency Calls by Time of Day

A city’s fire department expects that emergency call volumes vary by time of day according to histor

FRQ 12: Employee Training Program and Job Promotion

A company is investigating the effectiveness of its training program on job promotions. The collecte

FRQ 16: Association Between Marital Status and Voting Behavior

A study examines whether marital status is associated with voting behavior for Party X versus Party

FRQ 20: Investigative Task - Evaluating the Effectiveness of a Public Health Intervention

A public health department implemented an intensive smoking cessation program aimed at reducing resp

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

Genetic Trait Distribution Goodness-of-Fit

In a genetic cross the expected phenotypic ratio for a trait is 3:1 (dominant: recessive). A botanis

Genotype Ratios: Goodness-of-Fit Test in a Biology Experiment

In a genetic cross, the expected Mendelian ratio for three genotypes is $$1:2:1$$. In a sample of 16

Goodness-of-Fit Test for Web Traffic Sources

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

Homogeneity in Customer Service Satisfaction Across Branches

A retail chain wants to determine if customer satisfaction (Satisfied, Neutral, Unsatisfied) is homo

Homogeneity in Student Class Preferences

Three high schools conducted surveys to determine whether student preferences for online versus in-p

Independence of Smoking and Lung Disease

A public health survey collected data from 300 participants to investigate the relationship between

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

Manufacturing Defect Distribution Goodness-of-Fit

A factory produces items that may have one of four types of defects: Type A, Type B, Type C, and Typ

Market Research: Chi-Square Test for Homogeneity of Brand Choices

A market researcher wishes to determine whether consumer brand preference is consistent across three

Preferred Payment Methods: Chi-Square Test for Homogeneity

A market research firm conducted surveys in three different cities regarding preferred payment metho

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

Product Preference Independence Test by Gender

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

Social Media Platform Usage and Age: Test for Independence

A survey of 400 individuals collects data on their most-used social media platform (Platform A, Plat

Sports Preferences by Gender: Chi-Square Test for Independence

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

Traffic Accident Severity

In a study of traffic accidents on a highway, the outcomes were classified as Minor, Major, or Fatal

Vehicle Type Distribution Goodness-of-Fit Test

At a busy toll plaza, vehicles are classified into three types: Cars, Trucks, and Motorcycles. Based

Voter Preferences Across Regions: Homogeneity Test

A political analyst surveys 100 voters from each of three regions (North, South, Midwest) regarding

Voter Preferences Among Four Candidates – Chi-Square Goodness-of-Fit

An election poll of 800 voters reports the following counts for four candidates: Candidate A: 220, C

Voter Turnout by Age Group Homogeneity Test

A political scientist wants to compare voter turnout (Yes, No) across three age groups: Young, Middl

Workplace Safety Compliance

A company records the safety compliance of employees in two departments: Manufacturing and Administr

Advertising and Sales Revenue Regression Analysis

A marketing firm is studying the relationship between advertising spending (in thousands of dollars)

Advertising Budget and Sales Revenue

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

Advertising Data: Predicting Sales

A company wants to study how advertising spending (x, in thousands of dollars) affects product sales

Advertising Reach and Customer Acquisition

A digital marketing analyst studies the relationship between the number of advertising impressions (

Automobile Fuel Efficiency

A study analyzes the effect of engine displacement (in liters) on fuel efficiency (measured in miles

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,

Employee Salary and Years of Experience

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

Engine Size and Emissions

An environmental engineer is studying the relationship between engine size (in liters) and vehicle e

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

Fitness Tracker Study: Daily Steps and Weight Change

A fitness study examined whether daily steps (x, in thousands) predict weekly weight change (y, in p

Global Temperature Change

A climatologist studies the relationship between time (measured as years since 1900) and the average

Hours Practiced and Musical Performance Score

A music teacher is interested in whether the number of hours practiced per week is related to a stud

House Prices and Square Footage

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

Impact of Fertilizer Type on Plant Growth

A researcher is studying the effect of two different fertilizers on plant growth. The amount of fert

Internet Speed and Streaming Buffer Time

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

Machine Calibration and Defect Rate

A manufacturing engineer is studying the impact of a machine's calibration setting ($$x$$) on its de

Marketing Impact: Social Media Activity vs. Product Sales

A company collected data from 45 markets to investigate the effect of social media advertising hours

Marketing Spend and Customer Footfall

A retail company is examining whether there is a relationship between local advertising expenditure

Medication Dosage and Blood Pressure Reduction

A study investigates the effect of medication dosage (x, in mg) on blood pressure reduction (y, in m

Multiple Regression: Interpreting Slope in Presence of Collinearity

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

Practice Time and Music Performance Skill

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

Rainfall and Crop Yield

An agricultural study investigates the relationship between total rainfall (in inches) during the gr

Residual Analysis in Housing Price Regression

A real estate analyst uses regression to model housing prices based on various features. A residual

Software Development Efficiency: Lines of Code and Bug Count

A software company wants to study whether the number of lines of code written in a project is relate

Sports Performance: Practice Time vs Shooting Accuracy

A basketball coach investigates how weekly practice hours affect shooting accuracy percentages among

Stock Price and Market Index: Simulation of Slope Distribution

An economist is investigating the relationship between the daily returns of an individual stock and

Student Performance Analysis

A researcher investigates the relationship between the number of hours studied per week and improvem

Urban vs Rural Pollution Levels

An environmental study examined the relationship between daily traffic volume (in thousands of vehic

Water pH and Aquatic Life Diversity

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

Weekly Study Hours vs Exam Scores

A study evaluated the effect of weekly study hours on exam scores (out of 100) for a statistics cour

Wind Speed vs Power Output

An energy analyst is exploring the effect of wind speed (in m/s) on the power output (in kilowatts)