AP Statistics FRQ Room

Boxplot Comparison: Stock Price Fluctuations Over Years

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

Car Fuel Efficiency Test

A study measures the fuel efficiency of a sample of 50 cars. The sample has a mean miles per gallon

College Admissions Test Scores

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

College Graduation Rate Analysis

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

College vs. High School Sleep Study

Two surveys measured the number of hours of sleep per night. The high school survey recorded the fol

Comparative Analysis using Stem Plot and Histogram

Two groups of students took a standardized test. Group A's scores have a five-number summary: minimu

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

Effects of Adding a Constant on Measures of Spread

Consider the dataset of exam scores: {65, 70, 75, 80, 85}. Answer the following:

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

Event Attendance by Invitation Type

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

Exam Scores: Descriptive Statistics

A teacher collected the scores from a recent exam. The data are summarized in the frequency table be

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:

Internet Usage Among College Students

A survey of 220 college students recorded the number of hours they spend online per day. The results

Irrigation Techniques and Crop Yield

An agricultural study is set up to compare three irrigation techniques (drip, sprinkler, and flood)

Machine Adjustment Methods in Manufacturing

A manufacturing company wants to study the effect of two machine adjustment methods on production sp

New Product Defects

A new product is manufactured with a defect rate of $$0.01$$. In each production batch containing 50

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

Public Transportation Usage by Occupation

A survey of 240 workers recorded their public transportation usage (Regular, Occasional, Never) alon

Regression Analysis: Height and Shoe Size in Adolescents

A study on adolescents collected data on height (in cm) and shoe size. The least-squares regression

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.

Analysis of Two Categorical Variables in a School Survey

A high school surveyed 300 students to determine their favorite subject (Mathematics, Science, or En

Analyzing Temperature Effects on Electricity Consumption

A utility company collected data on average daily temperature (in °F) and electricity consumption (i

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

Coffee Shop Sales Analysis

A local coffee shop has recorded data on daily advertising expenditure (in dollars) and the correspo

Complex Survey Analysis: Income and Expenditure Patterns

A national survey collects data on household income (in US dollars) and monthly expenditure (in US d

Constructing a Contingency Table from Raw Data

A researcher surveying 100 individuals collected the following raw counts regarding gender (Male, Fe

Consumer Beverage Preference Analysis

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

Customer Service Evaluation: Categorical Analysis

A retail chain surveyed 300 customers regarding their overall satisfaction (Satisfied or Dissatisfie

Diet Soda Consumption and Weight Gain Analysis

Researchers examined whether there is an association between daily diet soda consumption (x, in lite

Employee Training Effectiveness

A company evaluated the effectiveness of two training methods by measuring subsequent job performanc

Environmental Awareness Survey

A survey was conducted to explore the relationship between recycling habits and environmental concer

Evaluating Coefficient of Determination in Athletic Performance

A study examining the relationship between weekly training hours (x) and athletic performance score

Exploring Temperature and Ice Cream Sales

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

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)

Nonparametric Alternatives to Linear Regression

Sometimes the assumptions of linear regression (such as linearity and homoscedasticity) are violated

Quality Control in Manufacturing

A factory produces light bulbs and historically 5% of bulbs are defective. A quality control inspect

Simulation Comparison of Unstandardized vs. Standardized Regression Coefficients

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

Temperature and Ice Cream Sales

A study over 30 days recorded the average daily temperature (in °F) and corresponding ice cream sale

Wait Time and Meal Satisfaction

A restaurant collected data from 40 customers on their wait time (in minutes) and meal satisfaction

Analyzing Sampling Variability with Box Plots

A study is conducted to estimate the average test score for teachers in a school district. Four diff

Bootstrapping the Sampling Distribution of a Mean

A researcher has collected exam scores from 15 students and wishes to estimate the sampling distribu

Cluster Sampling in Educational Research

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

Community Fitness Program and Weight Loss

A local government launches a community fitness program to help residents lose weight. The program i

Comparing Prospective and Retrospective Data Collection in Education Studies

A school district wants to study the impact of extracurricular activities on academic performance. T

Comparing Treatment Efficacy in a Retrospective Study

A retrospective observational study was conducted to examine the efficacy of two treatments for a pa

Comparing Two Treatments in a Medical Study

A clinical trial compares two treatments for lowering blood pressure. Treatment A (n = 25) results i

Customer Satisfaction Proportion Sampling

A company has found that 80% of its customers are satisfied with its service. A survey is conducted

Designing a Representative Student Survey

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

Designing a Stratified Sampling Plan for College Demographics

A university wants to estimate the average GPA for all its students. Given that the student populati

Exploring Stratified Sampling and its Sampling Distribution via Simulation

A researcher is studying a population that is divided into two distinct strata with different means.

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

Flu Vaccination Campaign and Illness Spread

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

Identifying and Mitigating Response Bias in a Health Survey

An online health survey asks participants about sensitive lifestyle behaviors such as alcohol consum

Impact of Advertising on Product Purchase

A company conducted a study on the effect of different advertisement types (Online, TV, Print) on pr

Investigating Voluntary Response Survey Bias

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

Modeling Nonresponse in Simulation of Sampling Distributions

A survey is conducted to measure the average household electricity usage. In the simulation, a rando

Prospective Cohort Study for Diabetes and Lifestyle Factors

A health organization plans to conduct a prospective cohort study to investigate how lifestyle facto

Replication in Experimental Designs: Water Purification Study

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Smoking Impact on Lung Capacity: Regression Study

Researchers are investigating the relationship between the number of years a person has smoked (x) a

Stratified Sampling in a City Demographics Study

A researcher intends to estimate the average household income within a large city by dividing the po

Survey Design: Improving Question Wording

A market research company is designing a survey for a new product but finds that several questions m

Temperature and Ice Cream Sales: A Summer Analysis

During the summer, a study was undertaken to analyze whether higher daily temperatures increase ice

Weather Patterns and Traffic Accidents

City officials are investigating the relationship between adverse weather conditions and the frequen

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

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

Basketball Free Throw Analysis: Binomial and Transformation

A basketball player has a free throw success rate of $$0.75$$ and takes $$16$$ free throws in a game

Comparing Average Test Scores of Two Teaching Methods

A study compares the effectiveness of two teaching methods in a school. Traditional teaching was use

Comparing Manufacturing Processes for Defect Reduction

An industrial engineer is comparing two manufacturing processes to determine which one produces fewe

Consumer Product Preference Analysis

A company surveyed 500 consumers about their preference for a new product. The results are summarize

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

Defective Products in Quality Control (Binomial Distribution)

In a quality control process, each product has a defect probability of 0.08 and is inspected indepen

Drug Effectiveness Study

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

Effect of Fertilizer Type on Plant Growth

An agricultural researcher is studying the effects of three different fertilizer types on plant grow

Employee Turnover Comparison in Two Departments

A company collected data on employee retention in two departments. In Department X, 45 out of 60 emp

Energy Consumption Random Variables

In a small town, the daily household energy consumption (in kWh) is modeled by the following distrib

First Purchase on a Website (Geometric Distribution)

On a website, each visitor makes a purchase with probability 0.03, independently of others. Let $$X$

Fitness Class Participation by Age Group

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

Hospital Stay Durations Analysis

A hospital collected data on the length of stay (in days) for patients following a particular surger

Impact of Meditation on Stress Reduction

A mental health clinic is studying whether an 8‐week meditation program reduces stress levels in its

Insurance Policy Sales Analysis

An insurance salesperson is tracking her daily sales. For auto insurance, the number of policies sol

Investigative Study on Public Health Intervention

A local government is assessing the effectiveness of a new public health campaign aimed at reducing

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

Pharmaceutical Study: Recovery Time Distribution

A pharmaceutical study records recovery times (in days) for a treatment with the following distribut

Restaurant Wait Time Assessment

A restaurant claims that the average wait time for a table is 15 minutes. However, a study of 25 tab

Scatterplot Regression Analysis on Advertising and Sales

A company collects data on its advertising budget (in thousands of dollars, x) and the resulting sal

Simulated Sampling Distribution of Survey Proportions

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

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

Testing a New App Feature through A/B Testing

A tech company is conducting an A/B test to evaluate a new feature that is intended to enhance user

The Impact of Sample Size on Outcome Predictability

A game organizer is designing a carnival game that involves tossing a fair coin. A player wins if th

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

Transportation and Work Patterns Survey

A survey of 500 people recorded their preferred mode of transportation and work location (Remote or

Understanding the Central Limit Theorem through Simulation

A simulation is performed where samples are drawn from various non-normal populations (for example,

Urban Traffic Volume and Air Quality

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

Urban Traffic Volume and Air Quality Regression Analysis

A city planner studies the relationship between daily traffic volume (in thousands of vehicles) and

Voter Turnout in Two Cities

A researcher collected data on the number of people who voted in two cities during an election. In C

Voting Behavior in Local Elections

A local election study collected data on voting behavior by political ideology. The summary is as fo

Battery Life Analysis Using Normal Distribution

A battery manufacturer claims that the lifespan of its batteries is normally distributed with mean $

Caffeine Content Analysis

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

Comparing Biased Estimators via Simulation Outcomes

A simulation study compares two estimators for a population parameter. Estimator A has a constant bi

Customer Complaints by Service Type

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

Difference in Sample Means: Genetic Mutations and Parental Age

Research indicates that 40-year-old men contribute an average of $$65$$ genetic mutations to their c

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

Evaluating Customer Satisfaction Proportions

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

Evaluating Genetic Mutations in New Fathers

A study examines the number of genetic mutations passed on by new fathers of different ages. It is e

Evaluating Sample Proportions in a Survey

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

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

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.

New Drug Effect on Blood Pressure Reduction

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

Polling Data Analysis

In a large election, the true support for a candidate is believed to be $$52\%$$. A random sample of

Psychological Test Reliability

A psychological assessment is administered to a random sample of $$50$$ individuals. The test has a

Sampling Distribution for Sample Proportions in Math Anxiety Study

A recent study estimates that 80% of people with high math anxiety experience brain activity similar

Sampling Distribution for Sample Proportions: Political Polling

In a political opinion poll, it is estimated that 55% of voters support a certain policy. A random s

Sampling Distribution of a Sample Proportion for Disease

In a health study, it is known that 5% of the population has a particular disease. A random sample o

Assessing Customer Satisfaction in a Retail Store

A retail store surveys 200 customers and finds that 150 are satisfied with their shopping experience

Comparative Study on Voter Turnout in Urban and Rural Areas

A study was conducted comparing voter turnout in urban and rural areas. In an urban sample of 400 re

Confidence Interval for Social Media Users

A survey was conducted on 800 individuals to assess daily social media usage. Out of 800 respondents

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 Loyalty Program Impact Study

A retail company introduces a new loyalty program and compares the proportion of customers making re

Customer Preference Difference Between Cities

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

Effectiveness of a Drug

A clinical trial is conducted to test the effectiveness of a new drug. In the trial, 400 patients we

Effectiveness of a Public Health Intervention: Investigative Task

A public health organization is assessing the effectiveness of a new intervention aimed at increasin

Employee Promotion Rates

A firm is comparing promotion rates between two departments. In Department A, 150 employees were sam

Environmental Policy Opinion Poll

A survey was conducted to assess public support for a new environmental policy. In an urban area (Gr

Estimating Customer Satisfaction

A local coffee shop surveyed 200 customers to assess their satisfaction. Out of the 200 customers, 1

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

Evaluating Errors in Proportion Tests for New Drug Effectiveness

In a clinical trial evaluating a new drug, the null hypothesis is that the drug has no effect on the

Health Survey Confidence Interval Analysis

A local health department conducted a survey regarding residents' compliance with a new health regul

Influence of Advertisement Exposure on Product Purchase

A marketing study examined whether exposure to an advertisement influences the likelihood of purchas

Interpreting a Confidence Interval

A study on dietary habits produces a 95% confidence interval for the proportion of adults consuming

Nutrition Labeling Impact Study

A government agency implements a policy requiring prominent nutritional labels on packaged foods. A

Online Shopping Behavior

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

Political Polling: Estimating Voter Support

In a random sample of 800 voters, 464 indicated support for Candidate A. Answer the following questi

Public Health Confidence Interval

A hospital conducted a simple random sample of 500 patients to gauge satisfaction with treatment qua

Public Health: Smoking Rates by Region

A public health researcher wants to compare smoking rates between two regions. In Region 1, a survey

Quality Control in Manufacturing

A manufacturing quality control team is checking the proportion of defective items in a production b

Quality Control in Manufacturing

A quality control study in manufacturing compares two plants. In Plant 1, out of 500 items produced,

Research on Smoking Cessation Program

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

Retail Store Customer Satisfaction Confidence Interval

A retail store conducted a customer satisfaction survey. A random sample of n = 400 customers was se

Satisfaction with Mobile App Features

A tech firm surveys 650 mobile app users and finds that 390 users are satisfied with the app feature

Significance Testing of Proportion Differences in Crime Rates

In a survey, 55 out of 200 residents in City A and 40 out of 250 residents in City B reported feelin

Social Media Usage by Gender

A survey compares social media usage among different genders. In a sample of 400 males, 320 use soci

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

Testing for a Rare Event Proportion

An environmental study collected 1000 water samples to test for a rare pollutant. Only 4 samples tes

Voter Approval Poll Design

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

Assessing Training Effects on Marathon Times

A sports scientist is evaluating the effect of a new training regimen on marathon finishing times. T

Average Daily Sales at a Retail Store

A retail manager records the daily sales (in thousands of dollars) over a period of 20 days. The sam

Battery Life Study

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

Battery Lifespan Comparison

Two battery manufacturers are being compared based on the lifespan of their batteries. For Manufactu

BMI and Systolic Blood Pressure Analysis

The scatterplot below shows data on body mass index (BMI, x-axis) and systolic blood pressure in mmH

Comparing Average Heart Rates in Two Exercise Regimens

A fitness study compared the effects of two different exercise regimens on heart rate. Group 1 (n =

Comparing Two Diets

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

Computer Downtime Analysis

A sales representative suspects that his company's computers have higher average non-operational (do

Effect of Medication on Blood Pressure: Paired Data Analysis

A study was conducted on 30 patients to evaluate the effect of a new medication on systolic blood pr

Effectiveness of a New Drug

A clinical trial was conducted to determine if a new drug reduces systolic blood pressure. For each

Effectiveness of Drug Treatments

A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients

Employee Productivity Analysis

A study compares employee productivity scores between two departments. Department 1 (n = 30) has a s

Employee Training Effectiveness

A company conducts a study to evaluate the effectiveness of a new training program. The program's im

Hospital Stay Duration Comparison

A hospital administration is examining the average length of patient stays in two independent units:

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

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

Light Bulb Lifespan Hypothesis Test

A company advertises that its light bulbs have an average lifespan of 1200 hours. A quality control

Machine Calibration Paired Data

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

Manufacturer's Claim on Product Weight

A manufacturer claims that its product has an average weight of 50 grams. A study measuring 40 produ

Medical Test Accuracy and Diagnosis

A hospital is assessing the accuracy of a diagnostic test that indicates 'Positive' or 'Negative' re

New Coffee Blend and Alertness Test

A beverage company is testing whether a new coffee blend improves alertness by reducing reaction tim

Nutritional Study on Caloric Intake

A nutritional study compares daily caloric intake between individuals on two different diets. Group

Plant Growth under Different Fertilizers

A botanist is studying the effect of a new fertilizer on plant growth. A random sample of 12 plants

Project Completion Times

A company is evaluating the effect of a process improvement by comparing project completion times be

Response Time in a Virtual Reality Task

A technology company is testing a new virtual reality (VR) system for gaming. They measure the respo

Screen Time and Eye Strain Analysis

The scatterplot below depicts data on daily screen time (in hours, x-axis) and reported eye strain o

Simulation from a Bimodal Population

A researcher is studying a population that exhibits a bimodal distribution (e.g., test scores from t

Technology Adoption in Businesses

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

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

Tennis Serve Speeds

A sports scientist is analyzing the serve speeds (in km/h) of a professional tennis player. A random

Weight Loss Confidence Interval

A nutritionist is studying the effectiveness of a new weight loss program. A random sample of 20 par

Analysis of Dietary Habits

A nutrition study investigates whether dietary preferences are homogeneous across four regions. The

Assessing the Fit of a Theoretical Distribution on Emergency Call Durations

Emergency call durations are categorized as Short (0–2 minutes), Medium (2–5 minutes), and Long (ove

Branch Service Quality

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

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%

College Major and Part-Time Job: Independence Test

A study examines the association between college major and part-time job status. The data collected

Comparing Exhibition Attendance Among Different Museums

Three museums host the same exhibition and record attendance in three categories: High, Medium, and

Customer Satisfaction Across Store Branches: Homogeneity Test

A retail chain with three branches (A, B, and C) surveys customer satisfaction with three response c

Customer Satisfaction Survey Across Store Locations

A retail company conducts a survey to assess customer satisfaction across three store locations: Nor

Drug Efficacy Across Regions: Homogeneity Test

A pharmaceutical company tests the effectiveness of a new drug in four regions. Each region conducts

Drug Side Effects Analysis: Chi-Square Test for Independence

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

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,

FRQ 1: Distribution of Customer Preference for a New Snack

A snack company claims that the preferences for flavors of its new snack follow the proportions: Fla

FRQ 4: Quality Control in Manufacturing Defects

A manufacturer claims that defects in its production process are distributed among three types: Type

FRQ 5: Health Supplement Side Effects

A double-blind clinical trial is conducted to compare a new health supplement with a placebo. Partic

FRQ 6: Association Between Diet and Heart Disease Risk

A study investigates whether there is an association between diet type and heart disease risk. The s

FRQ 13: Customer Loyalty Across Store Branches

A chain store wants to investigate whether customer loyalty is consistent across its four branches.

FRQ 18: Evaluating Distribution of Blood Types in a Sample Population

A hospital expects the distribution of blood types in the general population to be: Type O: 45%, Typ

Fruit Distribution Goodness-of-Fit Test

A fruit vendor claims that the distribution of fruits in a basket follows the percentages: 40% Apple

Genetics Research: Rat Coat Colors

In a genetics experiment, the expected Mendelian ratio for rat coat colors is 3:1 (dominant: recessi

Independence Test: Voting Preference and Gender

A survey of 500 voters collected data on voting preference (Candidate A, Candidate B, Other) and gen

Marketing Strategy Effectiveness

A company wants to assess if customer responses vary by the type of advertisement. Three ad types (O

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

Restaurant Choices Across Regions: Chi-Square Test for Independence

A customer satisfaction survey collected data from 600 diners across three regions (urban, suburban,

Simulated Chi-Square Distribution for Voting Patterns

A simulation study is conducted to examine the chi-square distribution under the null hypothesis tha

Social Media Platform Usage

A marketing agency expects that among 500 consumers, the usage of social media platforms is distribu

Sports Preferences by Gender: Chi-Square Test for Independence

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

Survey of Smartphone OS Usage

A national survey collected data from 400 respondents on their smartphone operating system preferenc

Survey on Preferred Modes of Transportation

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

Type of Transportation and Commute Satisfaction

A survey of 530 commuters collected data on their primary mode of transportation (Car, Bus, Bike, Wa

Voting Methods: Chi-Square Goodness-of-Fit

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

Workplace Safety Compliance

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

Advertising Budget and Sales Revenue

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

Advertising Budget and Sales Revenue

A marketing analyst is studying the relationship between a company’s monthly advertising budget (in

Advertising Expenditure and Product Sales

An economist investigates whether advertising expenditure (in millions of dollars) predicts product

Advertising Spending and Sales Revenue

A company collected data on its monthly advertising spending (in thousands of dollars) and correspon

Agricultural Yield Analysis

Agricultural scientists examine the effect of fertilizer application (in kg/ha) on crop yield (in to

Altitude vs Cooking Time

A culinary scientist is investigating whether altitude affects cooking time for a specific recipe. D

Biomarker Levels and Disease Severity Simulation

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

Car Age and Resale Value

A used car dealer is examining the relationship between a car's age (in years) and its resale value

Car Fuel Efficiency and Engine Size Comparison

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

Clinical Trial Dosage-Response Simulation

A medical researcher investigates the relationship between the dosage of a new medication (in mg) an

Customer Wait Time and Satisfaction Ratings

A call center is analyzing whether average wait time ($$x$$, in minutes) affects customer satisfacti

E-Commerce Website Traffic and Sales

An online retailer analyzes the relationship between daily website traffic (in thousands of visits)

Effect of Class Size on Student Achievement

An education researcher examines data from 50 classrooms to study the relationship between class siz

Effect of Study Habits on Exam Scores

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

Electricity Bill vs Temperature

A utility company studied the relationship between the average monthly temperature (in $$^\circ F$$)

Energy Consumption and Outdoor Temperature

A study on 30 households examined the relationship between outdoor temperature (x, in °F) and energy

Engineering: Stress and Strain in Alloys

In an experiment studying a new alloy, engineers measured stress (x, in MPa) and strain (y, dimensio

Environmental Pollution and Distance Simulation

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

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 and Temperature

A vendor analyzes the relationship between daily average temperature (in °C) and ice cream sales (in

Internet Speed vs. Streaming Delay

A study of 30 households examines the relationship between internet speed (in Mbps) and video stream

Interpreting Confidence Intervals from Multiple Studies

Two independent studies estimate the slope of a regression line that relates coffee consumption to p

Library Study Rooms Reservation vs Exam Success

A university service collected data on the number of library study room reservations made by student

Measurement Error Impact on Slope Estimation: Simulation Study

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

Plant Growth and Fertilizer Amount

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

Predicting Blood Pressure Based on Age

A health study collected data on systolic blood pressure (in mm Hg) and age (in years) for 40 adults

Regression Analysis in Real Estate Pricing

This question examines inference for the slope in a linear regression analysis between living area (

Sleep Duration and Reaction Time

A researcher studies the relationship between nightly sleep duration (in hours) and reaction time (i

Social Media Usage vs GPA

A researcher analyzed the relationship between weekly hours spent on social media and college GPA us

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 Study Hours and Exam Scores Simulation

A high school teacher is interested in how the number of hours spent studying affects exam scores. T

Study Hours and SAT Scores: Private vs Public

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

Technology Training and Productivity

A technology company wants to know if the number of training hours (x) influences employee productiv

Temperature and Ice Cream Truck Sales

An ice cream truck owner analyzes the relationship between the daily temperature (x, in °F) and ice

Traffic Volume and Pollution Levels

An environmental study was conducted over 45 days to assess the relationship between daily traffic v

Years of Experience and Salary Increase

A study investigated the relationship between years of job experience (x) and annual salary (in thou