AP Statistics FRQ Room

Almond Packet Weight Confidence Interval

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

Analysis of Categorical Data from Elections

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

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

Comparing Exam Score Distributions

Two classes took the same exam and their performances are summarized with back-to-back stemplots. Al

Comparing Measures of Variability: IQR vs Standard Deviation

Consider the data set: {12, 15, 18, 21, 24, 27, 30}. Answer the following:

Constructing a Frequency Histogram from Commute Times

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

Customer Ratings for Two Products

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

Customer Service Call Duration

Customer service call durations are approximately normally distributed with a mean of $$8$$ minutes

Customer Service Satisfaction by Service Type

A company surveyed 550 customers on their satisfaction level (Satisfied, Not Satisfied) with three t

Digital vs. Traditional Lesson Impact on Class Attendance

A school district is testing whether interactive digital lessons lead to higher class attendance tha

Empirical Rule Verification via Simulation

A professor is studying exam scores that are normally distributed with a mean of 70 and a standard d

Employee Salary Adjustments

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

Employee Turnover by Department

A company recorded employee turnover by department in a two-department organization (Sales and Engin

Hospital Wait Time

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

Hypothesis Testing: Reaction Time vs Age

In an experimental study on reaction times (in milliseconds) versus age (in years), the following re

Interpreting a Dot Plot of Daily Coffee Consumption

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

Measures of Variability in Teacher Ages

The ages of 12 mathematics teachers at a high school are: {24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 5

New Product Defects

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

Opinions on School Start Times

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

Parent Survey on School Length

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

Political Polling: Candidate Preference

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

Residual Analysis: Car Efficiency versus Engine Size

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

Sampling Distribution of the Sample Range for SAT Scores

A statistician is studying SAT scores whose distribution is known to have a certain degree of variab

School Year Length Preference Survey Analysis

A survey of 2000 parents was conducted asking their preference for the number of days in the school

Sports Participation and Club Membership

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

Survey on Favorite Ice Cream Flavors

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

Temperature and Reaction Rate Regression

A chemical kinetics experiment measured the reaction rate (in mol/sec) at different temperatures (in

Z-Scores and Percentile Ranks in a Test Examination

Assume that the scores on a standardized test are normally distributed with a mean of $$80$$ and a s

Analyzing Curvilinear Relationship and Data Transformation

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

Attendance and Test Performance

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

College Major by Gender

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

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

Comparing Regression Lines for Calorie Consumption in Two Groups

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

Comparing Two Regression Models for Chlorophyll Content Prediction

A biologist is studying the relationship between light intensity (x) and chlorophyll content in leav

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

Difference in Response Rates for Two Advertisements

A company tested two different advertisements on a website and recorded the number of clicks each ad

Elderly Health Program Evaluation

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

Experience and Salary: Exploring a Nonlinear Relationship

An HR department collects data on the number of years of experience (x) and annual salary (in thousa

Fitness Program Enrollment

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

Forest Fire Risk Analysis

In a forested region, each of $$1000$$ acres has an independent probability of $$0.005$$ of burning

Free Throw Performance in Basketball

A basketball player has a true free throw success rate of $$80\%$$. In one game, the player attempts

Impact of Sleep on Mental Health Scores

A psychologist investigates the relationship between the average number of hours of sleep per night

Inference on the Slope of Study Hours vs. Exam Score

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

Least Squares Regression for Predicting House Prices

A real estate analyst collected data on several houses detailing their square footage (X) and corres

Limitations of Simple Linear Regression

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

Medical Test Accuracy and Disease Prevalence

A certain disease affects 2% of the population. A diagnostic test for this disease has a sensitivity

Neighborhood Safety Survey

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

Political Preference by Demographic Group

A survey was conducted to explore the relationship between age group and political party preference.

Promotion Program Success Comparison

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

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

Reverse Regression: Predicting Hours Worked from Earnings

Consider a regression model for predicting earnings (Y, in thousands of dollars) from hours worked p

Simulating the Sampling Distribution of the Sample Range in Bivariate Data

A researcher is interested in exploring the sampling distribution of the range of response variable

Smartphone Brand Loyalty

A market survey examined customer satisfaction across three smartphone brands (Brand X, Brand Y, and

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,

Student-Teacher Ratio and Academic Performance

A school district collected data on 20 schools regarding their student-teacher ratio (x) and the ave

Website Click-Through Rate

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

Workforce Diversity Study

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

Analyzing a Charity Fundraising Event

A charity event recorded donations categorized by size (Small, Medium, Large) and by donor type (Fir

Assessing Sampling Techniques in Market Research for a New Product

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

Bias in Random Digit Sampling

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

Calculating and Interpreting a Confidence Interval from Water Quality Data

A study measures the concentration of a contaminant in a river. A random sample of 25 measurements y

Comparing Beverage Effects on Pulse Rates

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

Comparing Treatment Efficacy in a Retrospective Study

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

Customer Service Feedback

A company collected customer service feedback from three channels: Online, In-store, and Phone. The

Double-Blind Clinical Trial Design in Drug Efficacy

A clinical trial is set up to test a new drug's effectiveness in lowering cholesterol. The study is

Double-Blind Experiment Design for Nausea Reduction

A research team is testing a new wristband designed to reduce postoperative nausea. To eliminate pla

Effect of Diet on Cholesterol Levels

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

Effect of Noise Levels on Sleep Quality

An environmental study investigates the association between ambient noise level (in decibels, x) and

Evaluating a New Teaching Method

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

Evaluating Bias in a Sampling Process: Voluntary Survey

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

Evaluating Survey Question Wording Bias

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

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 a Training Program on Employee Productivity

A company measured employee productivity before and after a new training program. Two independent sa

Impact of Advertising on Sales Increase

A company wants to evaluate if exposure to an advertising campaign affects the likelihood of an incr

Impact of Advertising on Sales Revenue

A chain of retail stores seeks to understand the relationship between advertising expenditures (in $

Investigating Data Variability in Statewide Math Test Scores

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

Quality Control in Manufacturing

A manufacturing process produces items, each with a 2% chance of being defective. A quality control

Retail Store Checkout Efficiency Study

A study compared the average waiting time at checkout between two methods in a retail store. For the

Scatterplot Analysis and Regression Line Interpretation

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

School Lunch Programs and Student Health

A school district implemented a new lunch program designed to improve student health. A study is con

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 in a Traffic Accident Study

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

Voter Behavior: Support for Policy X Among Different Age Groups

A political survey measured support for Policy X among two age groups. In a sample of 150 young vote

Advertising Budget and Sales Regression Analysis

A company investigates the relationship between its advertising spending (in thousand dollars) and i

Charity Lottery Expected Value Calculation

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

Coffee Shop Latte Prices

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

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 Consumer Spending at Two Malls

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

Defect Rate Comparison between Two Factories

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

Diet Preferences and Health Outcome

A nutrition study surveyed 200 individuals regarding their diet and health outcome. The data are sum

Effectiveness of Public Health Announcements on Mask-Wearing Behavior

During a flu outbreak, a health department launches a public health campaign to encourage mask-weari

Event Planning and Rainy Days: Binomial Analysis

An event planner considers a month of 30 days where the probability of a rainy day is $$0.3$$, indep

Exercise Time and Cholesterol Level Regression Analysis

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

Insurance Policy Sales Analysis

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

Insurance Policy Sales Analysis

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

Movie Rating Analysis on Streaming Platforms

A survey was conducted to compare negative movie ratings on two streaming platforms. On Platform A,

Quality Control Binomial Process

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

Random Variable Transformation in a Carnival Game

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

Restaurant Tips: Analysis of Random Variables

In a restaurant, tips received follow this distribution: $$0$$ dollars (p = 0.1), $$5$$ dollars (p =

Restaurant Wait Time Assessment

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

Simulated Coin Toss Sampling Distribution

In a simulation experiment, you simulate flipping a fair coin multiple times to record the proportio

Simulated Sampling Distribution of Survey Proportions

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

Small Business Daily Revenue Analysis

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

Social Media Post Engagement

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

Study Time and GPA Regression Analysis

A university study examines the relationship between the number of study hours per week (x) and the

Transforming Payouts in a Carnival Game

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

Website Session Duration Analysis

A tech company is analyzing website usage and wants to estimate the typical duration of user session

Assessing Bias in Weight Measurements

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

Assessing Estimators for Baseball Weight

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

Caffeine Content Analysis

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

Caffeine Content in Energy Drinks

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

Comparing Clinical Trial Drug Effects

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

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

Consumer Reviews: Variability Analysis

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

Diet Preferences and Exercise Habits

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

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 Distributions

A data set of 50 observations is known to have a mean of $$100$$ and a standard deviation of $$15$$.

Effect of Sample Size on Variability

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

Environmental Concerns by Community Type

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

Environmental Study: Tree Heights

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

Estimating Average Commute Time

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

Estimator Bias: Maximum vs. Mean in Soccer Scores

A soccer coach considers using the maximum number of goals scored in a series of 10 games as an esti

Evaluating Manufacturing Estimators

A factory produces widgets with a true length of 150 mm. Five different estimators (A, B, C, D, and

Financial Returns: Biased vs. Unbiased Estimators

Investment analysts use two estimators to predict the expected return of a financial asset. Estimato

Genetic Mutations in New Fathers

It is estimated that 40-year-old men contribute on average $$65$$ genetic mutations to their offspri

Hospital Emergency Room Waiting Times

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

Interpreting p-values in a Clinical Trial

In a clinical trial testing a new drug, the null hypothesis states that the drug has no effect. The

Manufacturing Process Consistency and Variability

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

Naked Mole Rat Life Expectancy

The life expectancy of naked mole rats is normally distributed with a mean of $$\mu = 21$$ years and

Sampling Distribution for Sample Means: Caffeine Content in Energy Drinks

An energy drink has its caffeine content normally distributed with a mean of $$\mu = 200$$ mg and a

Sampling Distribution for Sample Proportions in a Survey

A survey indicates that 65% of viewers prefer streaming TV over cable. A random sample of 150 viewer

Simulated Sampling Distribution for Rare Events

A rare genetic marker is present in only 1% of a large population. A random sample of 200 individual

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

Simulation Study on Sample Variances

A simulation study is conducted to explore the sampling distribution of the sample variance $$s^2$$

Smartphone Battery Life Comparison

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

Survey on Preferred Beverage

A beverage company surveys 150 customers to estimate the proportion who prefer its new soda flavor.

Coffee Shop Loyalty

A coffee shop chain is investigating customer loyalty. A survey at the downtown branch (Group A) sam

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

Comparing Proportions in Education Methods

A study compares pass rates for students taught by two different methods. For Method A, 96 out of 12

Customer Loyalty Program Impact Study

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

Customer Satisfaction Survey

A company has collected customer satisfaction data from two sources. In-store customers (Group A) we

Customer Satisfaction Survey by Region

A retail company conducted a customer satisfaction survey in two regions, North and South. Responses

Effectiveness of a New Vaccine

A pharmaceutical company is testing a new vaccine. In a clinical trial, out of 1500 participants, 13

Environmental Study: Testing Proportion Exceeding Safety Threshold

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

Extremely High Support Rate Survey Analysis

In a survey of 500 voters, 485 express support for a new measure, resulting in a very high sample pr

Factory Quality Control Analysis

In a factory, quality control is carried out by inspecting a sample of items. Out of 800 items inspe

Health Intervention Program Effectiveness

A public health agency is evaluating a new intervention designed to increase the proportion of indiv

Hypothesis Testing and Errors: Sports Performance

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

Impact of a New Regulation

A government regulation is expected to reduce non-compliance among companies. In a survey conducted

Impact of Training Program on Certification Rates

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

New App Adoption Rate Confidence Interval

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

Opinion Poll on Environmental Policy

A survey of 600 citizens was conducted to gauge support for a new environmental policy. Out of the 6

Product Defect Rates in Manufacturing

A manufacturing plant operates two production lines. Line A produced 1000 items with a defect rate o

Restaurant Hygiene Survey Analysis

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

Retail Customer Satisfaction Survey Design

A retail chain wants to compare customer satisfaction levels between two store locations. A survey a

Sample Size Determination for Desired Margin of Error

A researcher wishes to estimate the proportion of households that recycle with a margin of error of

Study on Diet Preference Differences

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

University Enrollment Statistics

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

Voting by Race

A political science study collected data on voting behavior by race. Voters are classified as either

Average Monthly Rainfall

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

Clinical Drug Trial: Comprehensive Data Analysis

A clinical trial is conducted to compare the effect of a new drug versus a placebo in lowering chole

Coffee Shop Wait Times

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

Comparing Two Diets

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

Comparing Two Methods of Estimating Reaction Time

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

Comparing Two Treatments for Improvement

Two treatments for a health condition were tested. Group A (n = 40) experienced an average improveme

Comparison of Pollutant Concentration in Two Rivers

Environmental scientists measured the pollutant concentration (in mg/L) in two rivers. River 1 was s

Customer Wait Time in Service

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

Effectiveness of Drug Treatments

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

Election Polling Power Analysis

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

Evaluating a Sleep Intervention

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

Exam Score Analysis with Unequal Sample Sizes

A researcher compares exam scores between two sections of a course. Section A (n = 18) has a mean sc

Impact of New Traffic Signals on Commute Times

A city installs new traffic signals at a busy intersection to improve traffic flow. Traffic engineer

Investigative Analysis of Customer Service Performance Metrics

A company collects data on customer service performance across two centers. For a focused study on c

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

Manufacturing Process Improvement

A manufacturing company implements a new process intended to reduce component production times. For

Medical Test Accuracy and Diagnosis

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

Precision in a Manufacturing Process

A company claims that the mean diameter of a manufactured part is $$10$$ mm. An independent quality

Production Efficiency Comparison Across Shifts

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

Production Time and Number of Defects Analysis

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

Project Completion Times

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

Public Transportation Use and Environmental Awareness

A survey examines whether public transportation usage is related to environmental concern. Participa

Soil pH Variation

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

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

Testing Mean Daily Coffee Consumption Claim

A claim is made that college students drink an average of at least 2.5 cups of coffee per day. A sur

Training Hours and Employee Productivity Analysis

The scatterplot below shows data on training hours (x-axis) and employee productivity, measured in u

Voting Behavior and Political Affiliation

A study analyzes voting behavior among members of two political parties, Party A and Party B. The da

Weekly Hours Worked and Earnings Analysis

The scatterplot below displays data relating weekly hours worked (x-axis) to weekly earnings in doll

Weight Loss Confidence Interval

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

Academic Performance: Honors vs. Non-Honors

A school is investigating whether there is an association between program type (Honors vs. Non-Honor

Analysis of Dietary Habits

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

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

Book Genre Popularity Study

A survey by a local library aims to determine if the popularity of book genres matches the library's

Car Color and Accident Involvement: Independence Test

An insurance company collects data on car color and accident involvement among 500 policyholders. Th

Chi-Square Analysis of Traffic Light Phases

A transportation engineer hypothesizes that the timing of traffic light phases (green, yellow, red)

Customer Satisfaction Ratings Across Service Centers

Data has been collected from three service centers regarding customer satisfaction. The centers reco

Effectiveness of Advertisement Types

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

Election Polls: Goodness-of-Fit for Candidate Support Ratios

In a local election survey of 500 voters, the observed support percentages for candidates were: Cand

Employee Job Satisfaction by Department: Chi-Square Test for Homogeneity

A company surveys employees from three different departments (Sales, Engineering, HR) about job sati

Evaluating Marketing Strategies: Chi-Square Test for Independence with a Simulation Component

A marketing firm wants to determine if there is an association between consumer purchase behavior (B

Gender and Preferred Social Media Platform

A survey of 300 teenagers gathered data on their gender (Male, Female) and their preferred social me

Goodness-of-Fit Test for Web Traffic Sources

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

Homogeneity in Patient Recovery Rates Across Hospitals

Three hospitals recorded recovery outcomes for a specific surgery. The outcomes are categorized as S

Pet Ownership in College Residences

A study investigates whether there is an association between college residence type and pet ownershi

Quality Control in a Factory

A factory has three production lines, each producing 100 items. Quality control involves checking fo

Restaurant Menu Distribution Analysis

A popular restaurant chain claims that the distribution of orders among four cuisine types (Italian,

Species Distribution in Habitats: Chi-Square Goodness-of-Fit

A wildlife researcher hypothesizes that a species is distributed among four habitat types in a fixed

Sports Participation by Gender

A school survey collected data on sports participation among students, broken down by gender (Male,

Sports Preferences by Gender: Chi-Square Test for Independence

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

Teacher Satisfaction by Department: Chi-Square Test for Homogeneity

A school district wishes to determine if job satisfaction among teachers varies by department (Math,

Transportation Mode Among City Residents

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

Vehicle Type Distribution Goodness-of-Fit Test

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

Advertising Expenditure and Product Sales

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

Advertising Spend and Website Traffic

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

Agricultural Study: Fertilizer and Crop Yield

In an agricultural study involving 52 plots, researchers investigated the effect of fertilizer usage

Agricultural Yield Analysis

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

Biomarker Levels and Disease Severity Simulation

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

Coffee Consumption and Alertness

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

Crop Yields and Fertilizer Usage

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

Customer Satisfaction and Wait Times

A restaurant chain surveyed 50 customers to study the effect of wait time (x, in minutes) on satisfa

Dosage of Medication and Blood Pressure Reduction

A clinical researcher investigates whether the dosage of a new medication (in mg) is associated with

Dosage-Response in Drug Trials Simulation

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

Education Research: Impact of Class Size on Performance Simulation

An education researcher is investigating the impact of class size on average student test scores. A

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

Energy Consumption and Outdoor Temperature

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

Engine Size vs Highway Fuel Efficiency

An automobile researcher is studying the relationship between engine size (in liters) and highway fu

Exercise and Cholesterol Reduction

A health study investigated the effect of weekly exercise hours (x) on cholesterol reduction (y, 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

House Size vs House Price

A real estate analyst is studying the relationship between house size (in square feet) and house pri

Impact of Study Hours on Exam Scores

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

Manufacturing Defects and Operation Time

In a manufacturing process, data was collected to analyze the relationship between machine operation

Medication Dosage and Recovery Time

A clinical trial explores the impact of a new drug's dosage (measured in mg) on recovery time (measu

Predicting Ice Cream Sales from Temperature

In a study of 25 summer days, data were collected on daily maximum temperature (x, in °F) and ice cr

Rainfall and Crop Yield

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

Regression Analysis in Judicial Decisions: Predicting Recidivism Risk Scores

A study uses regression analysis to predict recidivism risk scores based on the number of prior offe

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

Relationship Between Study Hours and Exam Scores

A school counselor is investigating the relationship between the number of hours a student studies a

River Flow and Pollutant Concentration

Environmental scientists are studying the relationship between river flow ($$x$$, in cubic feet per

Robotics and Efficiency

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

Social Media Use and Academic Performance

A study examines whether daily social media usage (x, in hours) is related to students' GPAs (y, on

Stock Price and Market Index: Simulation of Slope Distribution

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

Student Performance and Study Hours

Researchers examine the relationship between hours studied (x) and exam scores (y). The regression a

Study Hours and SAT Scores: Private vs Public

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

Tree Growth Analysis: Simulated Slope Distribution

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