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

Analyzing Z-Scores and Normal Distribution

Assume that a particular set of data is normally distributed with a mean of 100 and a standard devia

Cumulative Frequency Graph Analysis for Age

A cumulative frequency graph is constructed for the ages of 100 individuals. The graph indicates the

Customer Satisfaction in Two Regions

A popular restaurant chain conducted a customer satisfaction survey in two different regions. The fo

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; $

Effect of Price Increase on Customer Participation

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

Employee Salary Adjustments

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

First Defective Product: Geometric Distribution

In a factory, each product has a 3% chance of being defective. Products are inspected sequentially u

Home Run Distances in Ballparks

The following set of home run distances (in feet) to center field in 13 ballparks is given: {387, 40

Interpreting Boxplots for Salary Data

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

Investigating Class Test Scores

A teacher collected the following test scores from a class: {55, 60, 62, 68, 70, 72, 75, 78, 80, 83,

Irrigation Techniques and Crop Yield

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

Job Satisfaction Across Departments

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

Leadership Training and Employee Satisfaction

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

Online vs. In-Person Instruction on Language Course Retention

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

Political Polling: Candidate Preference

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

Regression Analysis: Height and Shoe Size in Adolescents

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

Shopping Satisfaction: Online vs. In-Store

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

Simulation of Taxi Annual Mileage Sampling Distribution

A researcher is investigating the annual mileage driven by taxi cabs in a metropolitan area. The pop

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

Simulation of the Sampling Distribution of the Mean Number of AP Classes Taken

A study of 2200 high school seniors reports the number of AP classes taken as follows: 0 AP classes

Simulation to Construct the Sampling Distribution of the 25th Percentile

An athletic coach is interested in the lower 25th percentile (first quartile) of sprint times (in se

Social Media Campaign Effectiveness on Engagement

A company ran two social media campaigns to test engagement. In Campaign A, 250 out of 600 posts rec

Social Media Platform Usage by Gender

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

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

Temperature and Reaction Rate Regression

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

University Lecture Attendance Analysis

A survey of university lecture attendances includes data from 28 lectures, with an average attendanc

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

Analysis of Marketing Campaign Data: Sales vs. Advertisements

A company conducted a marketing campaign across several regions and recorded the amount spent on adv

Analyzing Social Media Usage and Self-Esteem

A psychologist is studying the relationship between daily time spent on social media (x, in minutes)

Assessment of Internet Usage and Academic Performance

A study examines the relationship between the number of hours college students spend online per day

Coffee Shop Drink Preference

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

Dietary Effects on Blood Pressure

A research study is being conducted to assess the effects of a low sodium diet on blood pressure amo

Evaluating Coefficient of Determination in Athletic Performance

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

Exploring Temperature and Ice Cream Sales

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

Food Safety Inspections in Restaurants

In a restaurant chain, historical data show that 10% of health inspections result in a violation. In

Impact of Skewness on the Sampling Distribution of the Sample Mean in Bivariate Data

A researcher collects data on household income (x) and spending on luxury goods (y), noting that inc

Impact of Sleep on Mental Health Scores

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

Interpreting the Sign and Magnitude of the Correlation Coefficient

A study examining the relationship between daily temperature (X) and ice cream sales (Y) finds a cor

Least Squares Regression for Predicting House Prices

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

Manufacturing Defects in Two Production Lines

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

Museum Visits and Visitor Satisfaction

A local museum surveyed 40 visitors about the number of times they visited the museum in the past ye

Predicting Fitness Improvement from Exercise Duration

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

Predicting Student Exam Scores from Study Hours

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

Recovery Rates in Medical Treatments

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

Simulation of the Mean Residuals in a Regression Model

In a regression analysis, residuals (the differences between observed and predicted values) are expe

Social Media Use and Academic Performance

A study was conducted on 50 high school students to investigate the relationship between daily hours

Sports Performance and Training Type

A study examines the association between athletes' primary training type (Strength Training, Enduran

Student Preference Survey

A school conducted a survey to determine students' favorite extracurricular clubs, recording two cat

Student Study Habits and GPA

A high school collects data from a random sample of 30 students to explore the relationship between

Study Hours and Exam Scores

A high school collected data on the number of hours students studied for an exam (x) and their corre

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

Analyzing Student Study Habits

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

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 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 Sampling With and Without Replacement in Simulation

A researcher simulates sampling from a finite population of 200 units. Two methods are used to draw

Effect of Noise Levels on Sleep Quality

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

Effects of Diet Programs on Weight Loss

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

Environmental Pollution and Respiratory Health

Public health officials are studying the relationship between exposure to particulate matter (PM2.5,

Impact of Sample Size on Variability

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

Interpreting Observational Study Data on Exercise and Blood Pressure

A study tracks daily exercise minutes and resulting changes in blood pressure for 100 adults over a

Mobile App User Engagement

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

Monte Carlo Simulation and the CLT

A researcher conducts a Monte Carlo simulation by drawing 1,000 random samples, each of size 30, fro

Observational Study on Dietary Habits and Exam Performance

A high school is interested in studying the relationship between students' dietary habits and their

Predicting Car Mileage from Engine Size

A study of 80 cars investigates the relationship between engine size (in liters, x) and fuel efficie

Public Health Intervention on Smoking Cessation

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

Salesperson Success: Geometric Probability

A salesperson meets potential customers, and the probability of making a sale during any meeting is

Sampling Methods in a Stratified Design

A researcher is studying the study habits of college students. The student population is divided int

Sampling Variability in Teacher Performance Evaluations

A school district collects teacher performance evaluations through student surveys. The administrati

School Lunch Programs and Student Health

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

Simulation of the Sampling Distribution of Proportions in Quality Testing

A factory produces light bulbs and each bulb is classified as defective or nondefective. A simulatio

Social Media Usage among Teenagers

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

Social Media Usage and Mental Health

Researchers are studying the impact of social media usage on mental health among teenagers. A survey

Study Habits and GPA: A Regression Analysis

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

Voting Patterns in a Retrospective Study

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

Website Traffic Sampling Distribution

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

Advertising Budget and Sales Regression Analysis

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

AP Exam Score Distribution: Cumulative Probability Analysis

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

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

Consumer Product Preference Analysis

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

Customer Satisfaction Survey on New Service Protocol

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

Defective Light Bulb Binomial Probabilities

Suppose the probability that a light bulb is defective is $$0.1$$. Consider independent selections o

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

Employee Training and Department Performance

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

First Purchase on a Website (Geometric Distribution)

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

Game Show Strategy with Random Variables

In a game show, contestants choose one of five boxes containing different cash prizes. The boxes con

Highway Construction: Expected Daily Miles

A highway construction project operates under varying weather conditions. On a clear day, workers la

Impact of Advertising on Consumer Behavior

A marketing firm investigated the effect of advertisement exposure on purchasing decisions. The foll

Manufacturing Quality Control for Defects

A factory produces electronic components, and historically the defect rate is expected to be less th

Medical Screening Test Accuracy by Gender

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

Public Opinion Survey on Local Issues

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

Restaurant Tips: Analysis of Random Variables

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

Small Business Daily Revenue Analysis

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

Tip Amounts from Different Meal Services

At a restaurant, a waiter receives tips from two independent services. For lunch, the tip is modeled

Traffic Accident Analysis

A city records the number of traffic accidents per day over a month. The observed distribution is gi

Transportation Delay Times

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

Understanding the Central Limit Theorem through Simulation

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

Urban Traffic Volume and Air Quality

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

Advanced Experimental Design in Teaching Methods

A researcher is investigating the effectiveness of two teaching methods by comparing student test sc

Assessing Estimators for Baseball Weight

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

Assessing Estimators in Quality Testing

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

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

College Major and Internship Experience

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

Comparing Juice Bottling Process

A juice company compares its bottling process with that of a competitor. A random sample of 50 bottl

Effect of Ambient Music on Restaurant Wait Times

A study examines the effect of ambient music on restaurant wait times. In a restaurant that plays am

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

Election Polling Proportions

In a pre-election survey, it is known that 52% of voters favor a certain candidate. A random sample

Evaluating Estimators for Baseball Weight

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

Hospital Patient Satisfaction by Department

A hospital surveyed patient satisfaction in three departments. The table below displays the number o

Impact of Sample Size on Variability

A researcher is analyzing daily website visits. In an initial study with 30 days, the sample standar

Manufacturing Process Consistency and Variability

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

Music Streaming Service Satisfaction

A music streaming service is comparing satisfaction levels between Free and Premium subscription use

Normal Approximation for Binomial Proportions

In a large survey, $$65\%$$ of respondents favor a new policy. In a random sample of $$100$$ respond

One-Sample vs. Two-Sample Sampling Distributions

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

Prediction Intervals in Regression Analysis

A regression analysis is performed to predict final exam scores based on study hours. The regression

Psychological Test Reliability

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

Quality Control in Manufacturing: CLT Application

A manufacturing plant produces metal rods whose lengths are not normally distributed, but have a pop

Sampling Distribution for Differences in Sample Proportions in Political Polling

In a political poll, two districts are surveyed. In District A, 60% of 500 voters support a policy,

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

Sampling Distribution of the Maximum: Weather Temperature Extremes

A climatologist is studying daily maximum temperatures in a city. The theoretical population maximum

Simulated Daily Sales Distribution

A retail store simulated its daily sales over several months. The resulting sampling distribution of

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

Simulation Study on Sample Variances

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

Unbiased Estimators: Evaluating Sample Slope

In a study of the relationship between hours studied and exam scores, a simple linear regression is

Blood Donation Campaign Study

A local health department funds two different public campaigns to increase blood donation rates. One

Campaign's Voter Turnout Comparison

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

Coffee Shop Loyalty

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

Comparing Participation Rates in Exercise Programs Across Cities

Two cities conducted surveys about participation in exercise programs. City X had 250 participants o

Comparing Test Pass Rates

A study compares the pass rates of two types of schools. The following table summarizes the results:

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

Customer Loyalty Program Impact Study

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

Customer Preference Difference Between Cities

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

Diet Choices by Gender

A survey was conducted to analyze diet choices among male and female participants. Participants were

Effect of an Advertisement on Purchase Intent

A company wishes to evaluate the impact of an advertising campaign on purchase intent. Before the ca

Ethnicity and University Major

A university survey collected data on student major (STEM vs. Humanities) and ethnicity (Underrepres

Evaluating a Confidence Interval in a Political Poll

A political poll of 1,000 registered voters finds that 540 support candidate A. Pollsters wish to cr

Healthy Meals Experiment Design

A college dining services wants to assess if a new healthy eating campaign increases the proportion

Impact of New Educational Program

A school district implemented a new teaching method aimed at improving student performance. In a stu

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.

Planning a Comparative Survey

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

Political Polling: Estimating Voter Support

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

Public Health Confidence Interval

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

Public Health: Influenza Vaccination Rates

A public health study compares influenza vaccination rates between urban and rural areas. In urban a

Public Health: Smoking Rates by Region

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

Research on Smoking Cessation Program

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

Restaurant Hygiene Survey Analysis

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

Smoking Cessation Campaign Study

A public health campaign aims to reduce smoking rates. A survey is then conducted to estimate the pr

Social Media Usage by Gender

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

STEM Club Gender Representation Study

A high school is investigating the proportion of female members participating in its STEM clubs. Par

Student Satisfaction in Two College Courses

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

Testing for Change in Voter Intent Over Time

An exit poll conducted before and after a major debate shows different levels of support for Candida

Traffic Accident Analysis

A study on traffic accidents examined the severity of accidents (Severe vs. Minor) and the driver’s

University Policy Support Analysis

A university claims that 60% of its students support a proposed policy change. A random sample of 20

Vaccine Hesitancy Survey Design

Public health officials are conducting a survey to estimate the proportion of individuals who are he

Voting Patterns on Renewable Energy

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

Advertising Spend and Website Traffic Analysis

The scatterplot below presents data on monthly advertising spending (in thousands of dollars, x-axis

Advertising Spending and Sales Regression Analysis

A researcher investigates the relationship between advertising spending (in thousands of dollars) an

Comparing 3-Point Percentage Rates

A sports analyst wants to compare the true 3-point shooting percentages of two basketball players. I

Comparing Two Diet Programs on Weight Loss

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

Computer Downtime Analysis

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

Customer Satisfaction at Two Store Branches

A retail chain collects customer satisfaction ratings (on a scale of 1 to 10) from two store branche

Effectiveness of a New Study Method on Test Scores

A tutoring program is implemented in a school, and the same group of 12 students is tested before an

Employee Productivity Analysis

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

Employee Training and Productivity Outcome

A company examines whether the type of training (Online vs. In-person) affects employee productivity

Fuel Efficiency of Hybrid Cars

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

Impact of a Diet Program on Weight Loss

A weight loss study measures the weight of 20 participants before and after a 6‐week diet program. T

Lifespan of New Light Bulbs

A company tests the lifespan of a new type of light bulb. A random sample of 18 bulbs shows a mean l

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

Nutritional Study on Caloric Intake

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

Online Shopping and Customer Satisfaction

A retail company conducted a survey to assess customer satisfaction with its online shopping experie

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

Pre- and Post-Intervention Test Score Analysis

An educational researcher wants to evaluate the effect of a new study program on student performance

Project Completion Times

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

Role of Random Sampling in Simulation Studies

A statistician conducts a simulation study by drawing 1000 random samples of size n = 25 from a data

Simulation of Sampling Distribution of Mean Reaction Times

In a cognitive psychology study, reaction times (in milliseconds) to a stimulus are collected. A sim

Simulation of the Sampling Distribution for Mean Salary

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

Testing Mean Daily Water Consumption

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

Analyzing Website Navigation: Chi-Square Test for Independence

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

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

Blood Type Distribution: Goodness-of-Fit Test

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

Car Color and Accident Involvement: Independence Test

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

Computer Usage and Major Association Independence Test

At a university, students are classified by their computer usage frequency (Low, Medium, High) and b

Consumer Brand Preference Homogeneity Test

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

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

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

Dietary Preferences Among Age Groups: Chi-Square Test for Independence

Nutritionists surveyed 300 individuals to examine if dietary preference (Vegetarian, Non-Vegetarian)

Evaluating Student Performance: Chi-Square Goodness-of-Fit in Grades Distribution

A large high school believes that the distribution of final letter grades (A, B, C, D, F) on a stand

FRQ 3: Voter Preferences by Age Group: A Homogeneity Test

A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup

FRQ 7: Comparing Satisfaction Levels Across Service Centers

A company wants to determine if customer satisfaction is consistent across three service center bran

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 Voter Turnout Among Demographic Groups

Exit polls in three different cities recorded voter turnout (Voted, Did Not Vote). Use the data to t

Independence Test: Technology Adoption and Age Group

A survey of 600 consumers categorized by age group (Young, Middle-aged, Senior) recorded whether the

Market Analysis: Brand Preference

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

Online Shopping Day Preferences: Chi-Square Goodness-of-Fit

A retailer surveys 150 online shoppers to determine which day of the week (Monday through Friday) th

Population Distribution: Rural, Suburban, and Urban

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

Product Defect Rates – Chi-Square Goodness-of-Fit

A quality control engineer hypothesizes that defects in a product occur with equal probability among

Quality Control: Defective Items in Production Lines

A factory operates 4 production lines. It is believed that the proportion of defective items is the

Restaurant Choices Across Regions: Chi-Square Test for Independence

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

Simulated Data: Random Number Generator Uniformity Test

A random number generator produced 1000 numbers that were binned into 10 equal intervals. The observ

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 Preference

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

Sporting Event Results: Homogeneity Test

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

Student Extracurricular Activities: Chi-Square Goodness-of-Fit

A high school believes that student interest in extracurricular activities (Sports, Music, Drama, Cl

Survey Response Distribution Goodness-of-Fit Test

A survey on public opinion regarding a new policy asks respondents to choose among Agree, Neutral, a

Test for Independence: Music Preference and Age Group

A survey of 300 individuals recorded their favorite music genre (Rock, Pop, Classical) and age group

Traffic Accident Severity

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

Transportation Mode Preferences: Homogeneity Test in City vs. Suburban Areas

An urban planner surveyed residents in a city and a suburban area about their preferred transportati

Advertising Budget and Sales Revenue

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

Advertising Expenditure vs Sales

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

Agricultural Study: Fertilizer and Crop Yield

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

Air Quality and Traffic Flow

A study investigates whether daily traffic flow (vehicles per hour) is associated with urban air pol

Coffee Bean Price and Quality Score

A coffee connoisseur collected data on the price per pound of specialty coffee beans (x, in dollars)

Coffee Consumption and Alertness

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

Coffee Consumption and Alertness Score

A nutrition study collected data on the number of cups of coffee consumed per day (x) and an alertne

Coffee Temperature vs Reaction Time

A study was conducted to examine the effect of coffee temperature (in $$^\circ C$$) on reaction time

Consumer Spending and Income Levels

An economist analyzed data from 60 households to study the relationship between household income (x,

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 Experience on Salary

A company collected data on employees' years of professional experience (x, in years) and their annu

Effectiveness of a New Drug on Blood Pressure

A pharmaceutical company is investigating whether a new drug reduces blood pressure as the dosage (i

Examining Crop Yield from Rainfall

Researchers are investigating the relationship between the amount of rainfall (in inches) during the

Exercise Time and Calorie Burn

A fitness app tracks the number of minutes spent exercising (x) and the number of calories burned (y

Fuel Efficiency and Car Weight

An automotive researcher is examining the relationship between a car's weight (in pounds) and its fu

Global Temperature Change

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

Hours of Training and Athletic Performance

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

House Price Prediction Simulation

A real estate analyst is studying the relationship between house price (in $\$\,$ thousands) and squ

Impact of Study Hours on Exam Scores

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

Impact of Teaching Methods on Math Performance

A school district is interested in determining whether a new teaching method improves performance on

Internet Speed and Streaming Buffer Time

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

Machine Calibration and Defect Rate

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

Medication Dosage and Blood Pressure Reduction

A hospital study evaluated the effect of increasing medication dosage on blood pressure reduction. T

Multiple Regression: Interpreting Slope in Presence of Collinearity

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

Online Course Hours and Final Grades

An educational researcher is modeling final course grades (y, in percentage) as a function of the nu

Predicting Student Performance with Attendance Rates

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

Regression Analysis in Real Estate Pricing

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

Relationship Between Exercise Time and Cholesterol

A health study examines the relationship between weekly hours spent exercising (x) and cholesterol l

Replicating Slope T-Test Using Summary Statistics

A researcher reports a sample slope of 2.5 with a standard error of 0.5 based on 12 observations. An

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 (

Sleep Hours and Reaction Time

A psychology experiment studies the effect of sleep duration (in hours) on reaction time (in millise

Social Media Engagement and Online Sales

An e-commerce company investigates the relationship between daily social media engagement (measured

Social Media Use and Sleep Quality

A study investigates the relationship between daily hours spent on social media (x) and nightly slee

Software Development Efficiency: Lines of Code and Bug Count

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

Speed and Fuel Efficiency

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

Student Performance and Study Hours

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

Temperature and Electricity Usage

A utility company is studying the relationship between the average outside temperature (in °F) and t

Traffic Volume and Pollution Levels

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

Water pH and Aquatic Life Diversity

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