AP Statistics FRQ Room

Blood Pressure Analysis in Clinical Trial

A clinical trial studying a new treatment records the blood pressure of 19 patients. The sample has

College Admissions Test Scores

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

College vs. High School Sleep Study

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

Comparing Cumulative Frequency Graphs for Age Distributions

Two cumulative frequency plots represent the age distributions of residents in a town for the years

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

Customer Coffee Satisfaction Interval

A coffee shop surveys 50 customers to rate their satisfaction on a scale from 1 to 10. The sample ha

Daily Caloric Intake Data Analysis

A nutrition study collected data on the daily caloric intake of 170 individuals. The results, broken

Daily Step Count Hypothesis Test

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

Employee Salary Adjustments

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

Evaluating a Histogram for Skewness in Temperature Data

A histogram shows the distribution of daily temperatures (in °F) during a summer month. The histogra

Examining Data Variability in Sports Statistics

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

Holiday Shopping Behavior: In-Store vs Online

During the holiday season, a survey was conducted on shopping behavior. Among 300 in-store shoppers,

Hospital Wait Time

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

Internet Usage Among College Students

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

Lottery Ticket Analysis

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

Movie Theater Attendance

Ticket sales at a movie theater are assumed to be normally distributed with a mean of $$150$$ seats

Nature Exposure and Mood Improvement

An environmental psychology study is designed to assess whether guided nature walks improve mood amo

NBA Team Wins: Distribution Assessment

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

Online Course Satisfaction Hypothesis Test

A university is evaluating the satisfaction level with its online course. In a survey of 200 randoml

Opinions on School Start Times

Two high schools surveyed their students to determine whether they favor a later school start time.

Political Affiliation and Media Consumption

A study surveyed 300 voters on their political affiliation (Party A, Party B, Independent) and their

Product Length Variability in Manufacturing

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

Quality Control in Manufacturing

A quality control inspector examines items on an assembly line. Each item has a 2% chance of being d

Regression Analysis: Blood Sugar and Calorie Intake

Researchers are studying the relationship between daily calorie intake and blood sugar levels measur

Salary Analysis: Effect of Raises on Mean Salary

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

Simulated Sampling Distribution of the Range from a Uniform Distribution

Consider a population with a uniform distribution on the interval [0, 1]. A simulation is performed

Simulation of the Sampling Distribution for the Sample Variance

Consider a normally distributed variable with a true variance of $$\sigma^2 = 16$$. A researcher sim

Social Media Platform Usage by Gender

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

Social Media Usage and Employee Productivity

A business is interested in evaluating whether limiting social media usage during work hours increas

Subway Train Arrival Times

Subway wait times are normally distributed with a mean of $$5$$ minutes and a standard deviation of

Teacher Age Distribution Analysis

The ages (in years) of 12 mathematics teachers are given as follows: {24, 25, 25, 29, 34, 37, 41, 42

Analysis of Influential Points in Athlete Performance Data

A sports scientist investigates the relationship between training hours (x) and performance score (y

Analyzing Curvilinear Relationship and Data Transformation

A botanist records the amount of fertilizer applied (x, in grams) and the resulting plant growth (y,

Analyzing Temperature Effects on Electricity Consumption

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

Attendance and Test Performance

A teacher collected data from 25 classes on average class attendance (in %) and average test scores

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

A data analyst uses the bootstrap method to approximate the sampling distribution of the regression

Calculation of Correlation and Linear Regression from Summary Statistics

A study examines the relationship between daily device usage (in hours, X) and a productivity score

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 Customer Survey Analysis

A coffee shop conducted a survey to determine customer preferences based on the type of beverage and

Comparing Marginal and Conditional Distributions in a Two-Way Table

A car dealership survey recorded data on car color and type. The dealership is interested in the dis

Customer Satisfaction and Purchase Frequency

A retail store surveyed 80 customers and found that the satisfaction rating (on a scale of 1-10) pre

Employment Rates of College Graduates

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

Environmental Awareness Survey

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

Geometric Distribution of Quick Transactions at a Bank

At a bank teller, the probability that a customer completes a transaction in less than 5 minutes is

Health Study on Diet and Activity

A health study investigated the relationship between diet type (Vegetarian vs. Non-vegetarian) and a

Highway Traffic Flow and Accident Rates

A study examined 25 highways to investigate the relationship between average daily traffic flow (x,

Housing Prices and Square Footage Analysis

A real estate analyst collected data on various houses regarding their square footage (in square fee

Job Training and Post-Training Wages

A job training program collected data from 30 participants on the number of training hours (x) and p

Pets and Stress Levels

A study investigated the relationship between the number of pets owned (x) and self-reported stress

Predicting Student Exam Scores from Study Hours

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

Quality Control in a Bakery

A bakery finds that historically 2% of its cookies are too hard. In a sample of $$100$$ cookies, let

Recovery Rates in Medical Treatments

A clinical trial was conducted to compare the recovery rates of patients using two different treatme

Regression Analysis of Movie Attendance and Concession Sales

A movie theater records daily attendance (x) and the number of concession sales (y, measured in hund

Residual Analysis in House Price Prediction

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

Restaurant Tip Analysis

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

Simulation of Bivariate Data with Varying Leverage Effects on Regression Coefficients

A researcher simulates bivariate data to explore how the presence of high-leverage points affects th

Simulation Study for Confidence Intervals in Linear Regression Predictions

A marketing analyst uses simulation to assess the performance of confidence intervals in predicting

Social Media Use and Online Privacy

In a study on digital behavior, participants were surveyed about their level of social media usage (

Study Time and Test Scores Relationship

A teacher collected data on the number of hours 25 students studied for a final exam and their corre

Agricultural Practices and Crop Yields

Farmers are considering an innovative agricultural practice that may increase crop yields. An observ

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

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

Analyzing Sampling Variability with Box Plots

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

Assessing Nonresponse Bias in Telephone Surveys

During a telephone survey on community health, only 40% of the contacted individuals respond. Answer

Assessing the Impact of Sampling Bias through Simulation

A researcher suspects that a nonrandom sampling method may introduce bias into estimates of a popula

Bias in Random Digit Sampling

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

Bootstrapping the Sampling Distribution of a Mean

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

Comparing Customer Satisfaction Across Two Store Locations

A retail company conducted a survey to measure customer satisfaction at two store locations, Store X

Comparing Two Sample Means in Drug Recovery

A study compares recovery times (in days) of patients treated with two different drugs. Drug A was g

Designing a Double-Blind Experiment for Nausea Reduction

A hospital wants to test whether applying a wristband with a small marble over a specific pressure p

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

Effect of Outliers on Sampling Distributions

In statistical analysis, outliers can notably influence the results of a study. Answer the following

Effects of Diet Programs on Weight Loss

Researchers compared the effectiveness of two diet programs versus a Control group in achieving sign

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.

Investigating Sampling Bias in a Voluntary Response Survey on Social Media Usage

A market research firm conducts an online survey where participants voluntarily respond to questions

Music Therapy and Stress Levels

A study is designed to test whether music therapy can reduce stress levels in adults. A double-blind

Physical Activity Levels by Region

A health study surveyed residents in different regions to assess their physical activity levels (cat

Placebo-Controlled Experiment in Nutritional Supplements

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

Public Health Intervention on Smoking Cessation

A city public health department wants to evaluate the effectiveness of a new anti-smoking campaign i

Remote Learning Effectiveness

At a high school, the impact of transitioning to remote learning on student test scores is studied u

Replication in an Agricultural Experiment

An agricultural scientist is testing the effectiveness of two fertilizers on crop yield. The experim

Screen Time and Anxiety Levels

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

Simulating Sampling Distributions for Quality Control in Manufacturing

A manufacturing company produces items that are expected to weigh $$500 \text{ g}$$ on average with

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 Usage among Teenagers

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

Stratified Sampling in a City Demographics Study

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

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 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

Traffic Flow Analysis

A transportation department uses systematic sampling to count the number of vehicles passing a check

Voting Preference Analysis

A political analyst collected data on voting preferences by age group. The table below shows the num

Water Quality and Fish Populations: Regression Analysis

An ecologist is studying the effect of water quality on fish populations in lakes. The regression an

BMI and Systolic Blood Pressure Regression Analysis

A study investigating the relationship between Body Mass Index (BMI) and systolic blood pressure (in

Car Purchase Decisions by Region

A car dealership surveyed buyers about their vehicle type by region. The data are summarized below:

Comparing Click-Through Rates of Two Advertising Campaigns

An online ad campaign was run using two different strategies. Campaign A achieved 210 clicks from 30

Comparing Consumer Spending at Two Malls

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

Comparing Simulation Results for Rainy Days

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

Cumulative Distribution Function Analysis for Daily Customers

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

Cumulative Probability Distribution in AP Exam Scores

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

Defect Rate Comparison between Two Factories

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

Evaluating a Mobile App to Promote Healthy Eating

A public health researcher is testing a mobile app designed to promote healthy eating habits. Volunt

Fitness Class Participation by Age Group

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

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

Game of Score Sums

Two friends play a game where Friend A draws a card with values {2, 4, 6} (each equally likely) and

High School SAT Scores Analysis

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

Highway Construction Productivity Analysis

The daily output of highway construction (in miles) depends on weather conditions as follows: | Wea

Impact of Study Habits on Test Scores

A teacher wants to examine if spending an extra 30 minutes reviewing material after class influences

Law of Large Numbers in Coin Toss Experiments

An experiment involves flipping a fair coin under different conditions. Consider two scenarios: one

Multi-center Clinical Trial for a New Vaccine

A large-scale clinical trial is conducted across several hospitals to evaluate the efficacy of a new

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

Simulating the Expected Value in a Lottery Game

Consider a lottery game with payouts given by the following probabilities: $$P(\$2)=0.5$$, $$P(\$5)=

Sleep Duration and Reaction Time Regression Analysis

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

Software Use in Organizations

A survey of 230 organizations recorded the primary operating system used in different departments. T

Stock Market Daily Returns

A particular stock’s daily percentage return is modeled by a discrete random variable with the follo

Survey Response Binomial Analysis

In a survey of $$50$$ respondents, each respondent has a $$0.65$$ probability of giving a positive r

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

Transforming Game Winnings

A game offers winnings with the following outcomes: | Winnings ($$\$\$$) | Probability | |---------

University Dining Hall Food Quality Survey

A survey of university dining hall patrons was conducted to assess food quality. Out of 200 responde

Weather Impact on Road Conditions

A study of road temperatures under different weather conditions produced the following results. Use

Website Redesign and Sales Conversion Rates

A company tested its website performance before and after a redesign. The old design resulted in 90

Bacterial Count in Water Samples

A water quality test measures the concentration of bacteria (in CFU per 100 ml) in a river. The popu

Biased and Unbiased Estimators in Quality Control

A company uses three estimators (A, B, C) to estimate the average weight of its packaged product. Th

Biased Estimator in Quality Control

A manufacturer uses an estimator to measure the maximum strength of a new material. A simulation of

Caffeine Content in Energy Drink Boxes

A store sells boxes containing six bottles of an energy drink. The caffeine content per bottle is no

Caffeine Content in Energy Drinks

A particular energy drink contains an average of $$200$$ mg of caffeine with a standard deviation of

Comparing Class Test Scores

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

Comparing Variability: Averages versus Individual Values

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

Confidence Interval and Sampling Distribution in Height Estimation

A researcher aims to estimate the average height of college students with a margin of error of $$1$$

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 Outliers on Sampling Distribution of the Mean

A dataset on household incomes is highly skewed due to extreme values. A statistician takes random s

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

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 Math Anxiety and Brain Activity

Research estimates that 80% of individuals with high math anxiety exhibit brain activity consistent

Genetic Mutations in New Fathers

A study estimates that 40-year-old men contribute an average of $$65$$ genetic mutations (with a sta

High Math Anxiety and Brain Activity

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

Political Opinion Poll on Policy Support

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

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

Quality Control of Widget Weights

A factory produces widgets with weights that are normally distributed with $$\mu = 100$$ grams and $

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

Voting Behavior by Gender

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

Advertising Impact on Brand Recognition

A company launched an advertising campaign in two regions. In Region 1, a post-campaign survey of 50

Analysis of Emergency Room Wait Times Satisfaction

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

Campaign's Voter Turnout Comparison

A political campaign is studying voter turnout in two neighboring cities. In City A, a survey of 400

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

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

Drug Efficacy in Clinical Trials

A clinical trial is evaluating the efficacy of a new drug. In a study of 400 patients, 340 showed im

Environmental Policy Opinion Poll

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

Estimating Social Media Usage Proportions

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

Online Course Completion Rates

Two online courses aim to improve student skills. In Course A, 240 out of 300 students completed the

Planning a Comparative Survey

A researcher intends to conduct a survey comparing two groups and wants to detect a minimum differen

Political Opinion Poll Analysis

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

Public Health Confidence Interval

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

Quality Control in Manufacturing

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

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

Simulation and Analysis for Rare Diseases

An epidemiologist is studying a rare disease with an estimated prevalence of 0.5%. They simulate dra

Smartphone Brand Preference by Income Level

A market research survey categorized respondents by income level and their preferred smartphone bran

Social Media Influence Study

A marketing firm is investigating whether exposure to a popular social media influencer affects the

Student Housing and Meal Plan

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

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. Suburban Crime Reporting Rates

A survey was conducted to compare feelings of safety in urban and suburban areas. In an urban sample

Vaccine Acceptance Rates

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

Voter Initiatives on Environmental Policy

In a survey about a new environmental policy, 600 voters were asked whether they support the initiat

Web Advertisement Click-Through Rates

An online marketing team is comparing the click-through rates of two advertisements. Ad A was shown

Advertising Budget and Sales Performance Analysis

The scatterplot below represents data on a company's monthly advertising budget (in thousands of dol

Average Monthly Rainfall

Meteorologists are interested in the average monthly rainfall in a particular region. A random sampl

Battery Life Analysis for a Smartphone Model

A manufacturer claims that its new smartphone model has an average battery life of at least $$9.5$$

Coffee Consumption and Alertness Scores

A study investigates whether coffee consumption affects alertness. Two independent samples are consi

Coffee Shop Wait Times

An urban coffee shop is interested in assessing its average customer wait time (in minutes) from pla

Comparative Analysis of Lecture Techniques Using Paired Data

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

Comparing Free-Throw Percentages of Two Basketball Teams

A sports analyst collects data on free-throw percentages of players from two basketball teams. For T

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

Delivery Times: Standard vs. Express Shipping

A logistics company wants to compare the average delivery times for its two shipping methods. Data c

Effectiveness of Tutoring Program Investigation

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

Impact of a Study Technique on SAT Scores

A high school implements a new study technique intended to improve student SAT scores. A group of 40

Impact of Advertising on Product Awareness

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

Impact of Training Programs on Test Scores

An educational study compares the effectiveness of two training programs (Program A and Program B) o

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

Machine Downtime Analysis

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

Mean Gas Mileage Confidence Interval

A car manufacturer wants to estimate the true mean gas mileage of a new model. A random sample of 12

Paired Data in Pre-Test and Post-Test Scores

A company runs a training program and measures employee performance before and after the program. Fo

Production Efficiency Comparison Across Shifts

A factory compares production times between two work shifts. Shift A has a sample mean production ti

Reaction Time One-Sample t-Test

A psychologist is testing whether a new stimulus affects human reaction times. In a study of 15 indi

Simulation of Sampling Distribution for Mean Crop Yield

An agricultural researcher is interested in the average crop yield (bushels per acre) of a particula

Simulation of Sampling Distribution for Mean Rainfall Amounts

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

Simulation of Sampling Distribution for Mean Recovery Time

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

Student Participation in Extracurricular Activities

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

Temperature and Water Consumption Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and water consumption in gallon

Testing a New Drug's Effect on Cholesterol Levels

A pharmaceutical company claims that its new drug lowers LDL cholesterol levels. In a study of 12 pa

Testing Mean Daily Water Consumption

A municipal claim states that the mean daily water consumption in a city is 150 liters. A survey of

Academic Majors and Study Habits

A university studies the relationship between a student's major (STEM, Humanities, Social Sciences)

Age Group and Exercise Habits

A fitness survey categorizes participants into three age groups (Teen, Adult, Senior) and records th

Animal Species Distribution in Habitats: Chi-Square Test

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

Blood Type Distribution: Goodness-of-Fit Test

A study of 400 individuals reports the following observed counts for blood types: O = 180, A = 120,

College Major and Part-Time Job: Independence Test

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

Customer Satisfaction Across Regions

A retail chain conducted a survey to assess customer satisfaction in three different regions: North,

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

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

Customer Satisfaction Across Store Branches: Homogeneity Test

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

Dice Fairness Goodness-of-Fit Test

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

Drug Efficacy Across Regions: Homogeneity Test

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

FRQ 12: Employee Training Program and Job Promotion

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

FRQ 19: Comparing Library Usage Patterns Among Departments

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

Market Analysis: Brand Preference

A market analysis firm surveyed 200 consumers to determine their preference among three competing br

Population Distribution: Rural, Suburban, and Urban

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

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,

Shopping Preferences: Homogeneity Test Across Regions

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

Simulating the Distribution of the Chi-Square Statistic

A researcher wishes to use simulation to approximate the sampling distribution of the chi-square sta

Smartphone Brand Market Share: Goodness-of-Fit Test

A survey of 200 smartphone users records their preferred brand among four brands: A, B, C, and D. Th

Smartphone Brand Preference

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

Socioeconomic Status and Book Reading Frequency: Independence Test

A survey of 600 individuals collects data on their socioeconomic status (Low, Medium, High) and book

Sporting Event Results: Homogeneity Test

A study investigates whether the win distribution among five tournament teams differs. Each team's r

Student Course Preference and Major

A university surveys 300 students to determine if course delivery preference (Online vs. In-Person)

Test for Independence: Political Opinions on Climate Change

A survey of 400 registered voters categorized by party affiliation (Democrats, Republicans, Independ

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 Impact on Sales

A retail company examines how daily advertising expenditure (in thousands of dollars) influences dai

Advertising Spending and Sales Revenue

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

Coffee Consumption and Alertness

Researchers are investigating the relationship between the number of cups of coffee consumed per day

E-Commerce Website Traffic and Sales

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

Educational Study: Supplemental Tutoring Effect

A school district wants to assess the impact of additional tutoring (x, in hours per week) on math t

Electricity Usage and Temperature

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

Energy Consumption Analysis

A utility company is investigating the relationship between outside temperature (in °F) and resident

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

Researchers are studying the impact of pollutant concentration (in parts per million, ppm) on the ra

Exercise Frequency and Resting Heart Rate

A fitness study collected data from 50 adults on the number of times they exercise per week and thei

Exercise Time and Weight Loss

A personal trainer examines whether the number of hours exercised per week is related to weight loss

Global Temperature Change

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

Housing Prices Prediction

A real-estate analyst investigates how the selling price of houses relates to their size (in square

Ice Cream Sales vs Temperature

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

Impact of Fertilizer Type on Plant Growth

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

Library Study Rooms Reservation vs Exam Success

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

Machine Runtime and Maintenance Costs

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

Medication Dosage vs Blood Pressure Reduction

A clinical researcher examined the effect of medication dosage (in mg) on blood pressure reduction (

Practice Time and Music Performance Skill

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

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

Rainfall and Crop Yield

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

Relationship Between Hours Studied and Test Scores

A study collects data from 30 students on the number of hours spent studying (x, in hours) and their

Retail Store Foot Traffic and Sales Revenue

A retail chain is studying the relationship between daily foot traffic (number of people) and daily

Sleep Hours and Cognitive Performance

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

Speed and Fuel Efficiency

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

Sports Performance: Training Hours and 100m Dash Times

For 20 professional athletes, a regression analysis was performed to predict 100m dash time (y, in s

Study Program Length and Post-Graduate Salary

A career advisor is studying whether the length of graduate programs (in years) is related to the me

Study Time and Exam Scores

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

Technology Training and Productivity

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

Water pH and Aquatic Life Diversity

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

Weather Forecasting: Humidity vs. Chance of Precipitation

Meteorologists studied the relationship between relative humidity (x, in percentage points) and chan