AP Statistics FRQ Room

AP Class Enrollment Analysis

In a school, 300 students were surveyed regarding the number of Advanced Placement (AP) courses they

Application of the Empirical Rule to IQ Scores

Assume that IQ scores are normally distributed with a mean of $$100$$ and a standard deviation of $$

BMI and Blood Pressure Regression Analysis

A study examines the relationship between body mass index ($$BMI$$) and systolic blood pressure for

Charitable Donation Timing by Age Group

A charity collected data on donation timings (Morning, Afternoon, Evening) and donor age group (Youn

College Admissions Test Scores

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

Comparative Analysis using Stem Plot and Histogram

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

Daily Caloric Intake Data Analysis

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

Effectiveness of a New Drug

A clinical trial is conducted to evaluate the effectiveness of a new drug in improving patient outco

Employee Salary Adjustments

A company’s six employee salaries (in dollars) are as follows: {3000, 7000, 15000, 22000, 23000, 380

Evaluating a Histogram for Skewness in Temperature Data

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

Holiday Shopping Behavior: In-Store vs Online

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

Hospital Wait Time

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

Interquartile Range and Boxplot Construction

Given the dataset: {12, 15, 16, 18, 20, 22, 25, 27, 30, 35}, perform an analysis of its distribution

Investigating Class Test Scores

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

Investigative Task: Public Park Usage Study

A city park department seeks to understand how weather conditions affect park attendance. They plan

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

NBA Team Wins: Distribution Assessment

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

New York City Taxi Mileage Distribution

Taxicabs in New York City are driven an average of 75,000 miles per year with a standard deviation o

Phone App Usage Times

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

Political Polling: Candidate Preference

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

Quality Control in Manufacturing

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

Rainfall Occurrence: Binomial Model

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

Sampling Distribution of the Median in a Skewed Production Process

A factory produces components whose lifespans (in hours) are right-skewed due to occasional defects.

Teacher Age Distribution Analysis

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

Teacher Ages Analysis

The ages (in years) of 12 mathematics teachers are: $$\{24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 54,

Z-Scores and Height Analysis

A researcher measures the heights of 50 students. It is found that the mean height is 160 cm with a

Advertising Spend and Website Traffic

A small business used data from 15 weeks to analyze the effect of advertising spend on website visit

Analyzing Temperature vs. Ice Cream Sales

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

Comparing Two Regression Models for Chlorophyll Content Prediction

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

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

Consumer Beverage Preference Analysis

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

Contingency Table Analysis: Cuteness Factor Study

In a study on the Cuteness Factor, 250 volunteers were shown pictures from three categories: Cute An

Customer Service and Order Mode Inference

In a survey at a local restaurant, 70 customers ordered online and 30 ordered in-person. Among the o

Designing an Observational Study: Screen Time and Sleep Quality

You are tasked with designing an observational study to investigate the relationship between daily s

Elderly Health Program Evaluation

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

Employee Training Effectiveness

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

Environmental Study: Air Pollution vs. Respiratory Issues

A public health researcher collects data from 50 cities to examine the relationship between air poll

Examining the Sampling Distribution of the Mean Difference in Two Groups via Simulation

A researcher collected test scores from two different classes with 30 students each. She wants to si

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

Job Training and Post-Training Wages

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

Online Course Enrollment Prediction

A university is analyzing the effect of the number of online advertisements (x) on online course enr

Political Preference by Demographic Group

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

Predicting Fitness Improvement from Exercise Duration

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

Residual Analysis in House Price Prediction

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

Restaurant Tip Analysis

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

Sampling Distribution of the Sample Range and Its Limitations via Simulation

A statistician is interested in exploring the sampling distribution of the sample range from a bivar

Simulation of Bivariate Data with Varying Leverage Effects on Regression Coefficients

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

Simulation of the Impact of Measurement Error on the Sampling Distribution of Pearson's r

A study measures the relationship between two variables, but with varying degrees of measurement err

Simulation-Based Investigation of Chi-Square Distribution in Two-Way Tables

A researcher is interested in the chi-square test for independence in a two-way table. To understand

Sports Performance and Training Type

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

Student Study Habits and GPA

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

Student-Teacher Ratio and Academic Performance

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

Study Techniques and Exam Performance

A researcher collected data on the number of hours college students spent using active study techniq

Temperature and Ice Cream Sales

An ice cream vendor records daily maximum temperatures (in degrees Fahrenheit) and the number of box

Analysis of Recycling Behavior

A survey was conducted to study recycling habits among individuals with different education levels.

Analysis of Smoking Habits Among Adults

A public health researcher surveyed adults and categorized them by age group (Young, Middle, Senior)

Analyzing Survey Bias in Voluntary Response Surveys

A local newspaper conducts a voluntary response survey asking residents about their satisfaction wit

Central Limit Theorem Demonstration Through Simulation with an Exponential Population

A researcher is interested in the Central Limit Theorem (CLT) and performs a simulation by drawing s

Clinical Trial on Weight Loss Programs

A randomized controlled trial compares two weight loss programs. Program A (n = 40) results in an av

Cluster Sampling in Educational Testing

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

Comparing Beverage Effects on Pulse Rates

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

Effect of Outliers on Sampling Distributions

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

Effects of Diet Programs on Weight Loss

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

Evaluating a New Teaching Method

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

Evaluating the Effectiveness of a New Drug

A clinical trial compared a new drug with a placebo regarding patient recovery. The data are summari

Flu Vaccination Campaign and Illness Spread

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

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 Undercoverage Bias in Voter Surveys

A national polling organization uses a telephone directory to sample voters for an upcoming election

Impact of Undercoverage Bias on Survey Results

A political poll is conducted by calling numbers from a telephone directory during evening hours, po

Manufacturing Processes and Product Lifespan

A manufacturing company is testing whether a new production process can increase the lifespan of its

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

Modeling Nonresponse in Simulation of Sampling Distributions

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

Retrospective Study Analysis on a Health Outbreak

Epidemiologists are conducting a retrospective study on a past health outbreak by analyzing existing

Retrospective Versus Prospective Public Health Studies

A public health agency is planning to study the spread of a novel pathogen. They have access to exte

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 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 Traffic Accident Study

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

Urban Green Spaces and Air Quality

An urban planning study is being conducted to determine whether proximity to green spaces is associa

Assessing the Impact of a New Advertisement Campaign

A retail company wants to measure the effect of a new advertisement campaign on store sales. A sampl

Carnival Game Payoff Transformation

In a carnival game, the payoffs are: $$2$$ dollars with probability $$0.5$$, $$5$$ dollars with prob

Coffee Consumption and Alertness Level Regression Analysis

A study examines the influence of coffee consumption (number of cups per day) on an individual's ale

Coffee Shop Latte Prices

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

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

Defective Lightbulbs: A Binomial Distribution Problem

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

Employee Training and Department Performance

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

Employee Turnover Comparison in Two Departments

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

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

Law of Large Numbers in Coin Toss Games

Consider a game where a player repeatedly flips a fair coin. The game has two winning conditions: In

Online Advertisement Click-Through

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

Random Variable Transformation in a Carnival Game

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

Reading Preferences by Genre and Format

A survey was conducted on reading preferences among 300 respondents. The survey collected data on pr

Sales Calls Geometric Distribution

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

Scatterplot Regression Analysis on Study Habits

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

Social Media Post Engagement

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

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 =

Transportation and Work Patterns Survey

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

Virus Spread Modeling among Animal Species

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

Weather Impact on Road Conditions

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

Website Navigation and Conversion Rates

A website conducted an A/B test with two versions (A and B) and recorded visitor conversion outcomes

Website Redesign and Sales Conversion Rates

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

Analysis of Athletic Performance Improvements

A coach is comparing the performance improvements of athletes following two different training progr

Assessing the Conditions for the Central Limit Theorem

A production facility records the number of widgets produced per day by a machine. The daily product

Biased and Unbiased Estimators in Quality Control

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

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 Drink Boxes

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

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

Central Limit Theorem in Quality Control

A flour packaging machine fills bags that are intended to weigh 50 pounds on average with a standard

Coffee Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Teaching Methods

A study compares the effectiveness of two teaching methods. For classes using Method A, test scores

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 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 Restaurant Remodel on Customer Behavior

A fast-food restaurant tested whether remodeling their premises had an effect on how much food custo

Effect of Sample Size on Variability

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

Estimating Average Commute Time

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

Evaluating Bias in Strength Estimation

A manufacturing process for components uses a new estimator to measure average component strength. A

Evaluating Math Anxiety and Brain Activity

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

Evaluating Sample Proportions in a Survey

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

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

In a survey, it is found that 40% of respondents own a smartphone. A random sample of 200 respondent

Favorite Ice Cream Flavor Survey – Sampling Proportions

In a survey on ice cream preferences, past research indicates that approximately 40% of respondents

Genetic Mutations in New Fathers

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

Hospital Patient Satisfaction by Department

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

Impact of Devices on Online Purchases

A study on online shopping examines whether the type of device used (Mobile or Desktop) is related t

New Drug Effect on Blood Pressure Reduction

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

Normal Approximation to the Binomial in Sampling Distributions

A factory has a light bulb defect rate of 2%. In a shipment of 500 bulbs, let X represent the number

Quality Control in Manufacturing: Sampling Distribution of Mean Weight

A factory produces metal rods with a mean weight of $$100$$ grams and a standard deviation of $$5$$

Sample Variance Distribution in Produce Weights

A study measures the weights of produce, where the population variance is known to be $$16$$ (kg^2).

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 Proportions: Political Polling

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

Simulation of Sampling Distributions: Dreams Recorded

A study finds that high school students remember an average of 3.4 dreams per night with a variance

Smartphone Battery Life Comparison

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

Social Media Usage by Age Group

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

Student Extra-Curricular Participation

A school conducted a survey to understand students' involvement in extracurricular clubs. The table

Analyzing Proportions as a Function of Batch Size

A manufacturing researcher is investigating the relationship between the size of a production batch

Assessing Website Conversion Rate

A company claims that its website has a conversion rate of 5%. To test this claim, a random sample o

Blood Donation Campaign Study

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

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 Methods for Quality Control in Manufacturing

A manufacturing company compares two quality control methods. In a trial run, Method A identified 95

Confidence Interval for Social Media Users

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

Customer Loyalty Program Impact Study

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

Employee Promotion Rates

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

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

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

Health Intervention Program Effectiveness

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

Health Survey Confidence Interval Analysis

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

Healthy Meals Experiment Design

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

Investigative Analysis of Consumer Behavior

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

Marketing Campaign Response Rate Test

A marketing team asserts that their campaign increases customer engagement, expecting a response rat

Medical Study: Confidence Interval for Treatment Success

In a clinical trial, 150 patients received a new treatment and 120 showed improvement. Construct a 9

Medical Study: Prevalence of a Risk Factor

A public health survey was conducted to determine the prevalence of a certain risk factor. In a simp

Opinion Poll on Environmental Policy

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

Physical Activity App Study

A startup company developed a new mobile application aimed at encouraging physical activity. Users a

Political Campaign Support Analysis

A political campaign conducted a survey to determine support for a candidate. In the survey, a simpl

Quality Control in Manufacturing

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

Retail Customer Satisfaction Survey Design

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

Retail Store Customer Satisfaction Confidence Interval

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

Social Media Influence Study

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

STEM Club Gender Representation Study

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

Study Habits and Course Success

A professor surveyed 200 students regarding their study habits and exam performance. It was found th

Voter Turnout Behavior Survey

A political organization implements a get-out-the-vote campaign in several precincts and wishes to d

Web Conversion Rate Analysis

A company is analyzing its website conversion rates over two consecutive months. In Month 1, 90 conv

Website A/B Testing

An online retailer is testing two versions of its webpage (Version A and Version B) to determine whi

Air Conditioning Energy Consumption

A manufacturer claims that its new air conditioning unit uses on average 6.5 kilowatts of electricit

Analyzing Machine Production Tolerances

In a manufacturing process, 15 measurements of a product dimension are recorded. The sample has a me

Career Development Program

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

Change in Manufacturing Process: Product Lifespan

A manufacturing company claims that a new manufacturing process increases the lifespan of its produc

Coffee Consumption and Alertness Analysis

The scatterplot below depicts data on the number of cups of coffee consumed per day (x-axis) and an

Comparative Analysis of Lecture Techniques Using Paired Data

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

Comparing Recovery Times in Two Hospitals

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

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

Computer Downtime Analysis

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

Daily Sales Confidence Interval

A store recorded its daily sales for 30 days, and the sample data yielded a mean of 200 units sold p

Daily Steps: Wearable Device Analysis

A fitness tracker company wishes to estimate the average number of steps taken per day by its users.

Drug Effectiveness on Blood Pressure

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

Effectiveness of Tutoring Program Investigation

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

Election Polling Power Analysis

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

Energy Consumption Analysis

An energy company is testing the claim that the average daily electricity consumption of households

Fuel Efficiency Analysis

A study is conducted to assess the fuel efficiency (in miles per gallon) of a new model of cars. A r

Impact of a Study Program on Exam Performance

A school introduces an intensive study program and measures students' exam scores before and after i

Impact of a Study Technique on SAT Scores

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

Income Analysis for a Tech Company

A tech company wants to estimate the average annual bonus received by its employees. A survey of 22

Investigating Student Reaction Times

A psychologist studies the reaction times of 30 college students using a computerized test. The meas

Monthly Sales Performance Analysis

A retail store assesses the impact of a promotional campaign on monthly sales. The data collected co

New Coffee Blend and Alertness Test

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

Paired SAT Score Improvement

An SAT prep course reports that its students improved their scores. In a sample of 30 students, the

Reaction Time One-Sample t-Test

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

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

Study Hours and GPA Analysis

The scatterplot below shows data on college students' weekly study hours (x-axis) and their GPA (on

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

Adoption Rates of Electric Vehicles by Region

A study compares the adoption rates of electric vehicles in three different regions: Urban, Suburban

Age Group and Exercise Habits

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

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

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

Consumer Brand Preference Homogeneity Test

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

Consumer Preference for Advertisement Types

A company believes that consumer preference for advertisement type follows the distribution: Online

Customer Satisfaction Survey Across Store Locations

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

DNA Mutation Distribution – Chi-Square Goodness-of-Fit

A geneticist hypothesizes that the distribution of DNA mutations in a sample of 300 cells is as foll

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

Examining Political Ideology: Chi-Square Test for Homogeneity

A political scientist collected data on ideological self-identification (Liberal, Moderate, Conserva

Favorite Ice Cream Flavor Goodness-of-Fit Test

A market survey hypothesizes that the favorite ice cream flavors are distributed as: Chocolate 40%,

FRQ 1: Distribution of Customer Preference for a New Snack

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

FRQ 11: Distribution of Emergency Calls by Time of Day

A city’s fire department expects that emergency call volumes vary by time of day according to histor

FRQ 13: Customer Loyalty Across Store Branches

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

FRQ 19: Comparing Library Usage Patterns Among Departments

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

Gender Distribution Across College Departments

A college collects data on faculty gender distributions across three departments. The data are as fo

Goodness-of-Fit Test for Dice Fairness

A six-sided die is suspected of being biased. In an experiment of 120 rolls, the observed frequencie

Manufacturing Defect Distribution Goodness-of-Fit

A factory produces items that may have one of four types of defects: Type A, Type B, Type C, and Typ

Preferred Study Methods: Homogeneity Test Across Colleges

Three colleges (X, Y, Z) surveyed students on their preferred study method: Group Study, Self Study,

Smoking and Exercise Frequency Independence Test

A health survey categorizes individuals by smoking status (Smoker, Non-Smoker) and exercise frequenc

Voter Turnout by Age Group: Test for Independence

A survey reports voter turnout among four age groups: 18-29, 30-44, 45-64, and 65+. The two variable

Advertising and Sales Revenue Regression Analysis

A marketing firm is studying the relationship between advertising spending (in thousands of dollars)

Advertising Spending and Sales Revenue

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

Blood Pressure and Sodium Intake Study

A study investigating the relationship between daily sodium intake (measured in mg) and blood pressu

Car Age and Resale Value

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

Climate Change: CO2 Concentration vs Global Temperature Simulation

A climate scientist is exploring how atmospheric CO2 concentration (in ppm) relates to global averag

Coffee Consumption and Alertness

A study examines the relationship between cups of coffee consumed per day (x) and a measured alertne

Coffee Consumption and Anxiety Levels

A psychologist investigates whether there is a relationship between the number of cups of coffee con

Coffee Temperature vs Reaction Time

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

Commuting Distance and Weekly Fuel Consumption

A transportation study collected data from 40 drivers to analyze the relationship between commuting

Consumer Spending and Income Levels

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

Effect of Study Habits on Exam Scores

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

Effect of Study Intervention on Academic Performance

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

Employee Salary and Years of Experience

A human resources analyst uses years of experience (x) to predict annual salary in thousands of doll

Engine Size and Emissions

An environmental engineer is studying the relationship between engine size (in liters) and vehicle e

Engineering: Stress and Strain in Alloys

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

Environmental Pollution and Distance Simulation

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

Exercise Duration and Heart Rate Recovery

A fitness researcher examines the effect of exercise duration (in minutes) on heart rate recovery ti

Exercise Time and Calorie Burn

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

Height and Weight Relationship: Male vs Female

A study investigates the relationship between height (in inches) and weight (in pounds) among male a

Hours of Training and Athletic Performance

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

House Prices and Square Footage

A real estate study uses the square footage of houses (x, in square feet) to predict their prices (y

Ice Cream Sales vs Temperature

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

Impact of Outliers on Slope Simulation

A statistician is studying the relationship between weekly physical activity (in minutes) and weight

Internet Speed vs. Streaming Delay

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

Interpreting Confidence Intervals from Multiple Studies

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

Manufacturing Defects and Operation Time

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

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

Modeling Blood Pressure Response to Medication Dosage

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

Physical Activity and Weight Loss: Simulation Analysis

A researcher is studying the effect of weekly physical activity (in hours) on weight loss (in kg) us

Relationship Between Exercise Time and Cholesterol

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

Relationship Between Study Hours and Exam Scores

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

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

Robotics and Efficiency

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

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

Student Performance and Attendance

A school administrator wants to understand the relationship between class attendance and test scores

Temperature Effect on Ice Cream Sales

An ice cream vendor recorded daily temperature (in °F) and daily ice cream sales (in dollars) over 3