AP Statistics FRQ Room

Comparing Cumulative Frequency Graphs for Age Distributions

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

Customer Ratings for Two Products

A market research firm collected customer ratings for two competing products. In a survey, 250 out o

Delivery Time Hypothesis Test

A fast-food chain advertises that its average delivery time is $$36$$ minutes. A consumer group coll

Effect of Constant Adjustments on Mean Salary

Consider the salaries (in dollars) of six employees given below: $3,000; $7,000; $15,000; $22,000; $

Exam Scores: Descriptive Statistics

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

Impact of Study Methods on Exam Performance

A school district plans a study to determine whether group study or individual study leads to higher

Job Satisfaction Across Departments

A company administered job satisfaction surveys in two different departments. In Department 1, 120 o

Marketing Campaign Reach by Region

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

Online vs. In-Person Instruction on Language Course Retention

An educational study is designed to compare the effectiveness of online versus in-person instruction

Parent Survey on School Length

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

Phone App Usage Times

Daily phone app usage is normally distributed with a mean of $$120$$ minutes and a standard deviatio

Rainfall Occurrence: Binomial Model

In a 31-day month (e.g., July), the probability of rain on any given day is $$0.2$$.

Restaurant Preference and Time Slot

A survey of 200 diners asked about their restaurant choice (Restaurant A or Restaurant B) and the ti

Salary Analysis: Effect of Raises on Mean Salary

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

Sampling Distribution and Confidence Interval Implications for Household Incomes

A sociologist is studying household incomes, which are right-skewed. The sociologist uses a simulati

Shipping Delays at a Warehouse

At a large distribution center, shipping delays (in hours) are approximately normally distributed wi

Shopping Satisfaction: Online vs. In-Store

A retail chain surveyed its customers to compare satisfaction between online shoppers and in-store s

Sports Participation and Club Membership

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

Stemplot Construction: Analyzing a Data Set

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

Stock Price Outlier Analysis

Consider the summarized daily stock prices (in dollars) of a company given by the following five-num

Unit Conversion Impact on Summary Statistics

A data set representing the lengths of objects is given in inches: {12, 24, 36, 48, 60}. Answer the

Analyzing Temperature vs. Ice Cream Sales

An ice cream shop collected data over a summer month to assess the relationship between daily temper

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

City Bicycle Usage Study

A city bike‐share program collected data on daily high temperatures (in °F) and the total number of

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

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 and Interpreting Prediction and Confidence Intervals

A study performs a linear regression analysis to predict exam scores (y) based on the number of prac

Customer Service Evaluation: Categorical Analysis

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

Daily Screen Time and Sleep Quality

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

Diet Program Success Rates

A nutritionist compared the effectiveness of two diet programs by surveying participants on whether

E-Commerce Site Traffic and Revenue Analysis

An e-commerce website collected data on daily visitor counts (x) and corresponding sales revenue in

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

Fitness Program Enrollment

A local gym evaluated enrollment trends by comparing two program types (Yoga vs. CrossFit) and atten

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

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

Interpreting a Simple Linear Regression Model in Advertising

A company studies the relationship between advertising spending (in $1000s) and sales revenue (in $1

Movie Genre Preference and Age Group

A survey of 200 moviegoers was conducted to investigate the relationship between movie genre prefere

Online Course Engagement and Performance

In an online course, data were collected from 40 students on the number of forum posts (x) and final

Online Learning Preferences

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

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

Sleep and Academic Performance

A study of 50 college students examined the relationship between hours of sleep (x) and GPA (y). The

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,

Study Habits and Exam Scores: Regression Inference

A study of 30 students collects data on hours studied (x) and exam score (y). The regression analysi

Urban Noise and Sleep Quality Study

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

Voter Approval Polling

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

Voting Behavior and Media Consumption

A political analyst surveyed 300 individuals to study the relationship between media consumption and

Website Click-Through Rate

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

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 the Impact of Sampling Bias through Simulation

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

Cluster Sampling in Educational Research

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

Cluster Sampling in Educational Testing

A school district with 50 schools wants to evaluate a new teaching method. They decide to randomly s

Commute Time and Job Satisfaction

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

Comparing Customer Satisfaction Across Two Store Locations

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

Comparing Test Scores Between Two Teaching Methods

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

Customer Feedback for a New Product

A technology company collected customer feedback regarding a new product via two purchasing channels

Customer Satisfaction with New vs. Old Product

A market research survey was conducted to compare customer satisfaction between a new product and an

Data Collection in a Prospective Observational Study

A hospital conducts a prospective study to evaluate recovery times following a specific surgical pro

Designing a Prospective Study on Exercise and Stress Reduction

A local fitness center aims to study the impact of a new exercise regimen on reducing stress levels

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

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

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

Effectiveness of a Training Program on Certification Outcomes

In a study evaluating a certification training program, 80 employees who attended the training had 6

Evaluating a New Teaching Method

A study compares a traditional teaching method and a new teaching method. In an independent study, 3

Experimental Design: Evaluating a Review Course for SAT Scores

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

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.

Impact of a New Diet on Blood Pressure

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

Impact of Sample Size on Confidence Interval Width

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

Interpreting a Scatterplot from a Survey on Sleep and Test Scores

A study surveys high school students regarding their average nightly sleep (in hours) and their most

Investigating Data Variability in Statewide Math Test Scores

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

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

Matched Pairs Design in Educational Research

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

Mobile App User Engagement

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

Participation in Extracurricular Activities

A school examines its students' participation in extracurricular activities by grade level (Junior v

Randomized Controlled Trial: Vaccine Efficacy

A clinical trial is conducted to evaluate a vaccine. 200 subjects receive the vaccine and 200 receiv

Simulation of the Law of Large Numbers

A classic coin-flipping experiment is simulated to illustrate the Law of Large Numbers. In the simul

Systematic Sampling in a Voter Preference Survey

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

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

Website Traffic Sampling Distribution

A website typically records an average of 100 visitors per hour with a standard deviation of 15 visi

AP Exam Score Distribution: Cumulative Probability Analysis

The table below shows the percentage of students achieving each AP exam score for a given year.

Basic Probability Rules in Testing Strategies

A standardized test uses different strategies when a student is uncertain about an answer. The table

Carnival Game of Chance: Payoff Transformations

A carnival game offers different monetary payoffs with the following probabilities: | Payoff ($$\$\

Carnival Game Payoff Transformation

In a carnival game, the possible winnings are $$2$$ dollars with probability $$0.5$$, $$5$$ dollars

Charity Lottery Expected Outcome

A charity sells 10,000 lottery tickets at $1 each with one prize of $7500. Let $$X$$ represent the n

City Traffic Speed Analysis

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

Coin Toss Experiment and Sample Size Effects

Consider an experiment where a fair coin is tossed repeatedly. Answer the following:

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 Click-Through Rates of Two Advertising Campaigns

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

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 Satisfaction Survey on New Service Protocol

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

Defective Lightbulbs: A Binomial Distribution Problem

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

Effects of Outliers on Sampling Distributions

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

Employee Training and Department Performance

A company recorded the outcomes of a recent employee training program across three departments. The

Exam Score Cumulative Distribution

The following table displays the distribution of scores on an exam from 200 students:

Exercise Time and Cholesterol Level Regression Analysis

A health study examining the effect of weekly exercise on cholesterol levels among 80 adults produce

Geometric Distribution in Reliability Testing

A machine in a factory has a 5% chance of failing on any given day. Let $$X$$ denote the day on whic

Highway Construction Work Analysis

A highway engineer observes that on a clear day, workers can lay $$5$$ miles of highway; on a rainy

Influence of Diet on Blood Pressure

A nutritionist is investigating how different dietary plans—specifically, low-carb, Mediterranean, a

Insurance Policy Sales Analysis

An insurance salesperson’s daily policy sales are modeled by separate probability distributions. For

Insurance Policy Sales Analysis

An insurance salesperson records her daily sales of auto and home insurance policies. The probabilit

Mobile App Daily Engagement

A mobile app developer claims that at least 40% of users engage daily with the app. In a random samp

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

Multistage Probability: Computer Viruses

On a university campus, computers run on different operating systems with the following distribution

Online Advertisement Click-Through

A digital marketing campaign delivers 200 ad impressions, where each impression has a 3% chance of g

Parental Involvement and Child's Academic Performance Regression Analysis

A study examines the effect of parental involvement (measured in hours per week) on a child's academ

Retail Customer Purchases: Random Variable Analysis

A survey at a retail store reveals that the number of items purchased per visit follows this distrib

Sales Calls Geometric Distribution

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

Sampling Distribution of the Interquartile Range (IQR) via Simulation

A simulation is performed to calculate the interquartile range (IQR) for samples drawn from a non-no

Scatterplot Regression Analysis on Study Habits

A researcher collects data on the number of hours students study (x) and their exam scores (y). The

Simulated Binomial Sampling Distribution

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

Simulation in Hypothesis Testing: Generating a Reference Distribution

A researcher employs simulation to generate the sampling distribution of a test statistic under the

Social Media Post Engagement

A social media analyst is studying the engagement on posts from a popular brand. A random sample of

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 Customer Satisfaction Claims

A coffee shop claims that 80% of its customers are satisfied. To test this claim, a random sample of

TV Advertising and Product Demand Regression Analysis

A company analyzes the relationship between TV advertising spending (in thousand dollars) and produc

Virus Spread Modeling among Animal Species

A study examines the spread of a virus among three animal species with the following data: | Specie

Assessing Estimators in Quality Testing

A factory uses different methods to estimate the maximum durable weight of a product. Five estimator

Blood Pressure Reduction Study

A study examines whether a dietary supplement affects blood pressure. In the supplement group, the a

Central Limit Theorem in Action: Distribution of Household Incomes

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

Comparing Clinical Trial Drug Effects

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

Comparing Mean Reaction Times Between Two Groups

A psychological study compares reaction times under two conditions. Group A (n = 40) has a mean reac

Comparing Sampling Distribution of the Sample Mean in Normal vs. Skewed Populations

Two populations, A and B, both have the same mean $$\mu = 100$$ and standard deviation $$\sigma = 20

Comparing Sampling Distributions from Two Populations

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

Comparing School Test Scores

School A has a test score distribution with a mean of 75 and a standard deviation of 8, and School B

Consumer Preferences for Soft Drinks

A market research firm collected data on consumer satisfaction for three soft drink brands. The tabl

Customer Complaints by Service Type

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

Effect of New Teaching Method on Student Scores

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

Effect of Sample Size on Variability

In a manufacturing process, the diameters of bearings are measured. Individual measurements have a s

Employee Productivity by Shift

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

Employee Training Program Evaluation

A company evaluated the effectiveness of its training programs by mode of delivery (Online vs. In-Pe

Evaluating Estimators for Baseball Weight

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

Graduation Rates by Gender

In a large school district, the graduation rate for girls is known to be 90%, while for boys it is 8

High Math Anxiety and Brain Activity

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

Math Anxiety Brain Activity Proportions

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

Normal Approximation Conditions for Solar Panel Households

A survey finds that 9% of households have solar panels. A random sample of 150 households is selecte

Quality Control in Baseball Production

A sports manufacturing company uses five different estimators (A, B, C, D, and E) to estimate the we

Sample Size Calculation for Voter Support Estimation

A political survey aims to estimate the proportion of voters supporting a specific candidate with a

Sampling Distribution for Differences in Sample Proportions: Political Polls

An exit poll surveys two candidates. Candidate X receives support of 48% from a sample of 400 voters

Sampling Distribution for Sample Means: Energy Drink Caffeine Levels

An energy drink has an average caffeine content of $$\mu = 200$$ mg with a standard deviation of $$\

Simulated Sampling Distribution of Sample Medians

A survey of 500 high school students collects data on the number of dreams remembered per night—a va

Social Media Usage by Age Group

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

Social Media Use and Sleep Duration

Researchers investigated the impact of social media use on sleep duration. Two independent groups we

Student Test Scores Sampling Distribution

An exam taken by a large group of high school students has scores that are approximately normally di

Voting Behavior by Gender

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

Website Load Time Evaluation

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

Advertising Impact on Brand Recognition

A company runs a new advertisement in two regions. In Region 1, 210 out of 350 respondents recognize

Assessing Customer Satisfaction in a Retail Store

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

College Acceptance Rate Comparison

Two high schools wish to compare college acceptance rates. School X admitted 75% of its applicants o

Comparing Satisfaction Between Two Stores

A retail chain wants to compare customer satisfaction between two of its stores. In Store A, 150 cus

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

A study compared the effectiveness of two teaching methods. In a sample of 150 students taught by Me

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

Designing a Survey for Voting Behavior

A political researcher plans to estimate the proportion of voters who will support a particular cand

Election Poll Margin of Error Analysis

An election poll reports a candidate's support proportion as 0.48 with a margin of error of 0.04 at

Government Policy Approval Confidence Interval

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

Health Study: Smoking Prevalence Comparison

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

Healthcare Plan Satisfaction

A survey was conducted among employees to assess satisfaction with their healthcare plans. Participa

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 for Hybrid Learning Preference

At a high school, a survey of 100 students reveals that 40 prefer a hybrid learning model.

Investigative Analysis of Consumer Behavior

A company undertakes a comprehensive marketing research project to analyze consumer behavior towards

Manufacturing Process Comparison

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

Online Advertising Effectiveness

An online marketing team is testing two versions of an advertisement. In a sample of 500 viewers for

Online Course Completion Rates

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

Restaurant Hygiene Survey Analysis

A local health department collected data on restaurant hygiene. In a simple random sample of 100 res

Retail Coupon Usage Among Customers

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

Service Reliability Study Analysis

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

Voting Patterns on Renewable Energy

A survey was conducted in two states regarding support for renewable energy initiatives. In State X,

Web Advertisement Click-Through Rates

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

Assessing a New Teaching Method

A study compares two teaching methods to assess their impact on student performance. In a randomized

Blood Pressure Reduction Confidence Interval

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

Career Development Program

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

Clinical Trial on Blood Pressure Reduction

A clinical trial is conducted to compare the effectiveness of two medications in reducing blood pres

Comparing Delivery Times

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

Comparing Recovery Times in Two Hospitals

A study compares patient recovery times (in days) following a standard surgical procedure at two dif

Customer Preference on Smartphone Features

A market research survey evaluates customer satisfaction for two smartphone brands, Brand A and Bran

Delivery Times: Standard vs. Express Shipping

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

Diet Choice and Energy Levels

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

Drug Effectiveness on Blood Pressure

In a clinical trial, 35 patients are given a new drug and their blood pressures are measured before

Election Polling Power Analysis

In an election poll, a candidate claims to have 70% support. A critic believes the true support is 6

Examining Teaching Methods

A school is comparing two teaching methods: Traditional and Modern. Student outcomes are classified

Fuel Efficiency of Hybrid Cars

A car manufacturer claims that its new hybrid model achieves an average fuel efficiency of at least

Gas Mileage Analysis: Confidence Interval Assessment

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

Impact of Training Programs on Test Scores

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

Machine Calibration Paired Data

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

Medical Test Accuracy and Diagnosis

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

Physical Activity and Cholesterol Levels

A nutritionist studies the impact of physical activity on cholesterol levels by comparing two groups

Production Time and Number of Defects Analysis

The scatterplot below displays data on production time in minutes (x-axis) and the number of defects

Quality Control: Machine Calibration

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

Rainfall Measurement Study

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

Reaction Time Hypothesis Test

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

Simulating Sampling Distribution of the Sample Range

A quality control analyst in a factory runs a simulation study by drawing 1000 samples of size n = 1

Simulating the Effect of Sample Size on Confidence Interval Precision

A statistician performs a simulation study to examine the effect of sample size on the precision of

Soil pH Variation

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

Test Score Improvement Analysis in a Preparation Class

In an SAT preparation class, 25 students took a pre-test and a post-test. The improvements (post-tes

Testing Mean Daily Water Consumption

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

Weight Reduction Program Evaluation

A fitness center evaluates its new weight reduction program by measuring the weights of 15 participa

Age Group and Exercise Habits

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

Assessing the Fit of a Theoretical Distribution for Disease Rates

A health researcher claims that the incidence of a particular disease in a population is distributed

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

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

Clothing Preference and Gender: Test for Independence

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

Dietary Preferences Across Regions

A nutrition study surveyed residents from three cities to determine their dietary preferences: Veget

Extracurricular Participation and Academic Performance Independence Test

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

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

Genetics Research: Rat Coat Colors

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

Goodness-of-Fit for Beverage Preferences

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

Insurance Claim Types: Independence Test Across Age Groups

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

Pet Ownership and Residence Type Independence Test

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

Phone Usage and Preferred App: Chi-Square Test for Independence

A tech survey collected data on 250 smartphone users on two categorical variables: phone operating s

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

Subscription Plans and Customer Region – Chi-Square Test for Independence

A streaming service collects data on customer region (North, South, East, West) and their chosen sub

Test for Independence: Political Opinions on Climate Change

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

Voter Initiative Support Homogeneity Test Across Regions

A study examines voter support for a new initiative in three regions: North, Central, and South. Ind

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

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

Advertising Data: Predicting Sales

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

Advertising Expenditure vs Sales

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

Age and Reaction Time Study

A cognitive psychology study examines the relationship between age (in years) and reaction time (in

Altitude vs Cooking Time

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

Coffee Consumption and Reaction Time Study

A study was conducted to examine the relationship between the number of cups of coffee consumed by c

Crop Yield and Fertilizer Application

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

Crop Yields and Fertilizer Usage

Agricultural researchers are investigating the effect of fertilizer amount (in kg per hectare) on cr

Daily Water Intake and Blood Pressure

A nutrition researcher studied the relationship between daily water intake (in liters) and systolic

Diet Plans and Weight Loss

A nutritionist compares the effectiveness of two diet plans by analyzing weight loss (in pounds) ove

Educational Study: Supplemental Tutoring Effect

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

Effect of Study Intervention on Academic Performance

Researchers are evaluating whether participation in a new tutoring program predicts improvements in

Electricity Bill vs Temperature

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

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

Exercise Duration and Weight Loss

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

Fertilizer Use and Crop Yield

An agricultural researcher studies the effect of fertilizer use ($$x$$, in kg/ha) on crop yield ($$y

Fish Population and Pollution Levels

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

Food Intake and Weight Gain in Mice

In an experiment with mice, researchers study the relationship between daily calorie intake ($$x$$)

Hours of Training and Athletic Performance

A sports scientist examines the relationship between hours of training per week ($$x$$) and athletic

Impact of Study Hours on Exam Scores

A study examines the effect of weekly study hours ($$x$$) on exam scores ($$y$$) among 30 students.

Machine Calibration and Defect Rate

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

Machine Runtime and Maintenance Costs

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

Manufacturing Quality Control: Regression Parameter Optimization Simulation

A quality control engineer is analyzing the relationship between machine operating speed (in m/s) an

Marketing Impact: Social Media Activity vs. Product Sales

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

Medication Dosage and Blood Pressure Reduction

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

Modeling Blood Pressure Response to Medication Dosage

A medical study investigates the effect of medication dosage (x, in mg) on the reduction in systolic

Online Advertisement View Time and Purchase Likelihood

A study examines the relationship between the time spent viewing an online advertisement ($$x$$, in

Plant Growth vs Fertilizer Amount

An agronomist is studying the effect of fertilizer amount (in kg/ha) on plant growth (in cm) in a co

Practice Time and Music Performance Skill

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

Predicting Sales Based on Advertising Budget

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

Predicting Student Performance with Attendance Rates

A teacher collects data on student attendance rates (x, in percentage) and corresponding performance

Relationship Between Temperature and Energy Consumption

A study of 30 households examined the relationship between the average outdoor temperature (in °F) d

Retail Store Foot Traffic and Sales Revenue

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

River Pollution Levels and Industrial Activity

An environmental scientist is investigating whether the level of industrial activity along a river (

Stock Price and Market Index: Simulation of Slope Distribution

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

Study Abroad Duration and Language Proficiency

A language institute studies the effect of time spent abroad (x, in months) on language proficiency

Technology Training and Productivity

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

Tree Growth Analysis: Simulated Slope Distribution

An ecologist is studying the relationship between the age of trees and their heights. The ecologist

Weight Loss and Diet Adherence

A nutritionist is studying the relationship between the number of diet counseling sessions attended