AP Statistics FRQ Room

Analysis of Categorical Data from Elections

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

AP Enrollment in High School

A survey of 2200 high school seniors recorded the number of AP classes each student is taking. The d

Cafeteria Food Satisfaction Proportion

A college cafeteria conducted a survey to estimate the proportion of students who are satisfied with

Calculating Variance and Standard Deviation for Book Counts

The numbers of books read by 10 students in a month are recorded as: {3, 4, 2, 5, 6, 4, 3, 3, 4, 5}.

Comparing Sleep Hours: High School vs College

Two surveys were conducted comparing the nightly sleep hours of high school and college students. Th

Consumer Smartphone Preferences Analysis

A survey was conducted at a shopping mall where 300 shoppers were asked about their preferred smartp

Customer Satisfaction in Two Regions

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

Dotplot Representation of Home Run Distances

A dotplot displays the following frequencies for home run distances (in feet): • 387 appears once •

Effectiveness of a New Drug

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

Effects of Multiplicative Transformations on Test Scores

A data set representing test scores is given as follows: {45, 55, 67, 73, 82, 88, 90}. Answer the fo

Employee Salary Adjustments

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

Event Attendance by Invitation Type

An event organizer tracked attendance based on invitation type (Digital, Paper) and the outcome (Att

Exploring Daily Sales Data Using a Stem-and-Leaf Plot

A small business has recorded its daily sales (in dollars) over 15 days. The data are summarized in

Hypothesis Testing: Reaction Time vs Age

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

Impact of Outliers on Measures of Center

Two datasets represent the annual household incomes (in thousands of dollars) in two similar neighbo

Interface Redesign and User Engagement

A tech company is testing whether a software interface redesign leads to higher user engagement. Use

Investigative Task: Evaluating a School Breakfast Program

A school district is considering a breakfast program aimed at improving student performance. Prelimi

Marketing Campaign Reach by Region

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

Mobile Device Battery Life

The battery life of smartphones is normally distributed with a mean of $$10$$ hours and a standard d

Normal Distribution: Taxi Mileage

Taxicabs in a large city are driven an average of $$75000$$ miles per year with a standard deviation

Online Shopping Preference by Age Group

An online survey collected responses about shopping behavior by categorizing respondents into age gr

School Year Length Preferences Survey

A survey is conducted among 2000 parents regarding their preferred school year length. The frequency

Shipping Delays at a Warehouse

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

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 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 Platform Usage by Gender

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

Study Program Effectiveness Hypothesis Test

A researcher wants to determine if a new study program increases test scores. In a random sample of

Teacher Ages Analysis

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

Treatment Outcomes in Hospital Study

A hospital conducted a study on two treatments (Treatment X and Treatment Y) to evaluate patient out

Advertising Spend and Website Traffic

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

Analyzing Social Media Usage and Self-Esteem

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

App Usage Trend: Free vs Premium Users

A tech company is studying how frequently users utilize a particular feature in their app. Two group

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

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

Constructing and Interpreting Prediction and Confidence Intervals

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

Customer Satisfaction and Purchase Frequency

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

Difference in Response Rates for Two Advertisements

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

Environmental Study: Air Pollution vs. Respiratory Issues

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

Exercise and Stress Investigation

A health research team collected data from 40 adults regarding their weekly exercise hours (quantita

Impact of a New Study App on Academic Performance

A technology company has developed a new study application intended to improve academic performance.

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

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 Study Methods on Test Performance

A university is interested in determining the effect of different study methods on students' perform

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

Medical Test Accuracy and Disease Prevalence

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

Movie Genre Preference and Age Group

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

Museum Visits and Visitor Satisfaction

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

Political Polling: Approval Ratings

A polling organization is studying the approval ratings of a political leader among urban and rural

Political Preference by Demographic Group

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

Predicting Apartment Rents

A real estate company collected data on apartment sizes (in square feet) and their monthly rents (in

Restaurant Tip Analysis

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

Retail Promotions: Sales vs Advertising Budget

A retail chain recorded weekly data (n = 20) on advertising budget (x, in thousand dollars) and week

Simulating the Sampling Distribution of the Sample Mean in Bivariate Data

A study collects data on the number of study hours (x) and exam scores (y) for 100 students. Researc

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

Sleep and Academic Performance

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

Specialty Coffee Orders at a Coffee Shop

At a coffee shop, 25% of customers order a specialty coffee. In a random sample of $$60$$ customers,

Transformation to Achieve Linearity in Population Growth

The following data show the estimated populations (in thousands) of a city at different years: | Ye

Transformation to Achieve Linearity: Population Growth

A rapidly growing town has recorded its population over a series of years, as shown in the table bel

Willingness to Adopt Electric Vehicles

A market research study investigated whether income level influences the willingness to adopt electr

Analysis of Recycling Behavior

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

Analyzing Bias in Convenience Sampling at a Mall

A researcher conducts a convenience survey at a local shopping mall to gauge consumer satisfaction w

Analyzing Student Study Habits

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

Cluster Sampling in Educational Research

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

Comparing Retrospective and Prospective Studies in Outbreak Analysis

An epidemiological study is being designed to investigate factors contributing to a recent influenza

Comparison of Test Preparation Courses on SAT Scores

A high school is comparing the effectiveness of two different test preparation courses on improving

Diet, Weight Loss, and Regression Analysis

A nutritionist is studying the relationship between daily caloric intake (Calories) and observed wei

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

Environmental Study on Pollution Levels

A retrospective study examined water quality from 40 rivers in a region, measuring the concentration

Estimating Average Park Visit Duration

A study is conducted to assess the average length of time (in minutes) that visitors spend at a loca

Impact of Sample Size on Confidence Interval Width

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

Implementing Simple Random Sampling

A researcher has a list of 500 registered voters and wants to conduct a survey about voter preferenc

Investigating Effects of Population Variability on Sampling Distributions

Two populations have the same mean $$\mu = 100$$ but different standard deviations: $$\sigma_1 = 10$

Measurement Reliability in Climate Data Collection

A climate study collects rainfall data from multiple sensors distributed across a region. The sensor

Mitigating Response Bias in Online Consumer Surveys

A company is conducting an online survey to gather customer satisfaction ratings for a new product.

Online Ad Click-Through Rates and Sampling Distributions

An online advertising campaign has a click-through rate of 5%, and a webpage receives 500 visitors i

Online vs. In-Person Shopping Preferences

A market research company surveyed shoppers to understand their preferred mode of shopping (Online v

Quality Control in Manufacturing

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

Quality Control in Manufacturing

A factory produces light bulbs. A quality control inspector takes a simple random sample of 200 bulb

Random Assignment in a Placebo-Controlled Medical Trial

A medical researcher plans a clinical trial to test the effectiveness of a new drug for migraine rel

Randomized Block Design in Evaluating a Teaching Method

A school district is conducting an experiment to compare a new teaching method with the traditional

Retrospective Study on Environmental Exposure and Health Outcomes

A public health researcher is studying the relationship between long-term exposure to poor air quali

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

Understanding Sampling Error through Repeated Sampling

A researcher repeatedly draws independent simple random samples of size 50 from a large population w

Advertising Budget and Sales Regression Analysis

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

Car Purchase Decisions by Region

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

Carnival Game of Chance: Payoff Transformations

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

Casino Free Chips: Pooling Strategies

At a casino, two individuals each draw a card from separate bags. Bag $$X$$ contains the numbers {$$

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

Comparing Daily Step Counts: Traditional Pedometer vs Fitness Tracker

A study compared the daily step counts of two groups: one group used a traditional pedometer (n = 50

Defects from Two Machines

A factory has two machines producing gadgets. Machine A produces 100 gadgets per hour with a defect

Dice Roll Sum Analysis

Two standard six-sided dice are rolled, and the sum $$X$$ of the numbers is recorded.

Drug Efficacy in Clinical Trial

A pharmaceutical company claims that at least 70% of patients will show improvement after receiving

Game Show Strategy with Random Variables

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

Geometric Distribution: Encountering an Honest Man

In a certain ancient society, the probability that a randomly selected man is honest is $$0.12$$. As

Highway Worker Productivity

A construction team has three possible outcomes for the number of miles of highway built in a day: 4

Insurance Sales Analysis

An insurance salesperson's daily sales for auto and home insurance are represented by two independen

Manufacturing Process Downtime

A factory records daily machine downtime (in hours) due to equipment failures according to the follo

Monthly Supermarket Expenditures

A local supermarket chain wants to estimate the average monthly expenditure of its customers. A rand

Parental Involvement and Child's Academic Performance Regression Analysis

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

Small Business Daily Revenue Analysis

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

Student Study Hours and Exam Performance Regression Analysis

A researcher examines the relationship between the number of hours a student studies (x) and their e

Student Testing Strategy and Scores Analysis

A standardized literacy test consists of 100 multiple-choice questions. When uncertain, test takers

Study Time and GPA Regression Analysis

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

Television Viewing Habits by Age and Time of Day

A survey of 300 television viewers recorded their preferred viewing times (Morning or Evening) acros

Testing Customer Satisfaction Claims

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

The Impact of Sample Size on Outcome Predictability

A game organizer is designing a carnival game that involves tossing a fair coin. A player wins if th

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,

Virus Infection in Library Computers

In a large library, computers run different operating systems with the following proportions: 50% ru

Website Conversion Rates: A/B Testing

An online retailer is testing two different webpage designs. Landing Page A received 120 conversions

Assessing Estimators in Quality Testing

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

Biased Estimator in Manufacturing

In a factory, two different devices (Device X and Device Y) are used to measure the length of metal

Caffeine Content Analysis in Energy Drink Boxes

An energy drink contains caffeine distributed with a mean of 200 mg and a standard deviation of 10 m

Caffeine Content in Energy Drinks

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

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

Coffee Consumption and Alertness

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

Comparing Juice Bottling Process

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

Comparing Sampling Distributions from Two Populations

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

Differences in Sample Means for Weight Loss Program

In a weight loss study, two groups are compared. Group A (n = 35) follows a new diet and has a sampl

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 Restaurant Remodel on Customer Behavior

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

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

Examining Bias in Sample Maximums

In a quality control study, an analyst records the maximum defect size from samples of 10 items take

Impact of Devices on Online Purchases

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

Lightbulb Life Expectancy Analysis

A certain brand of lightbulbs has a life expectancy that is approximately normally distributed with

Naked Mole Rat Life Expectancy

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

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 Conditions for Solar Panel Households

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

Prediction Intervals in Regression Analysis

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

Quality Control in Baseball Production

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

Quality Control of Widget Weights

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

Smartphone Battery Life Comparison

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

Student Performance and Study Techniques

A study compared two study methods: using flashcards versus summarization. In the flashcards group (

Training Techniques and Marathon Finish Times

A sports scientist is comparing the effectiveness of two training methods on marathon finish times.

Air Quality Health Survey Design

A public health department is conducting a survey to estimate the proportion of residents suffering

Assessing the Fairness of a Die

A six-sided die is rolled 600 times to test for fairness. In these 600 rolls, the result "6" appears

Assessing Website Conversion Rate

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

Comparing Hospital Readmission Rates

Two hospitals report their 30-day readmission rates. Hospital A had 60 readmissions out of 200 patie

Confidence Interval for a Population Proportion

A public opinion poll designed to estimate the proportion of voters who support a new policy produce

Customer Satisfaction Survey – Comparing Two Stores

A retail company conducted a customer satisfaction survey at two different store locations. At Store

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

Effect of an Advertisement on Purchase Intent

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

Effect of Sample Size on Margin of Error

A researcher is investigating the effect of sample size on the margin of error when estimating a pro

Effectiveness of a Drug

A clinical trial is conducted to test the effectiveness of a new drug. In the trial, 400 patients we

Evaluating Trends in Graduation Rates

Over a span of 10 years, a school district has recorded the annual graduation rates. A scatterplot o

Factory Quality Control Analysis

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

Government Policy Approval Confidence Interval

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

Political Polling: Estimating Voter Support

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

Public Survey on Recycling: Urban vs. Rural

A public survey investigated recycling habits in two different areas. In an urban area, 180 out of 3

Retail Coupon Usage Among Customers

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

Sample Size and Margin of Error Trade-Off Analysis

A political analyst is planning a poll and is considering two sample sizes. One sample of 300 respon

School Lunch Program Participation

A school district is evaluating participation in its free lunch program. In a sample of 250 students

School Lunch Program Participation

A study examines participation in school lunch programs in two schools. In School X, 60 out of 150 s

Service Reliability Study Analysis

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

Social Media Campaign Engagement Analysis

A company runs a social media campaign aiming for a target engagement rate of 40%. In a sample of 60

Social Media Survey on Privacy Concerns

A survey conducted on a popular social media platform asked 800 users if they are highly concerned a

Sports Participation by Gender and Sport Type

A survey collected data on sports participation, recording the favorite sport type as either 'Team S

Testing for a Rare Event Proportion

An environmental study collected 1000 water samples to test for a rare pollutant. Only 4 samples tes

Type I and Type II Errors in a Drug Trial

In a clinical trial of a new drug, the null hypothesis states that the drug's side effect rate is 10

University Policy Support Analysis

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

Voter Preference Comparison: Confidence Interval and Hypothesis Test

In a study of voter preferences, two independent samples were taken. In District A, a sample of 200

Air Conditioning Energy Consumption

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

Average Daily Reading Time of Students

A study investigates the daily reading habits of a group of students. In a random sample of 30 stude

Caffeine Consumption and Reaction Times

A study aims to determine whether the consumption of caffeine affects reaction times. Two independen

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 Consumption and Alertness Analysis

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

Difference in Mean Cholesterol Drop between Diet Plans

A nutritional study compares two diet plans. For Diet A, a sample of 50 participants shows an averag

Effectiveness of a New Drug on Pain Relief

A pharmaceutical trial tests a new drug intended to alleviate pain. In a double‐blind study, 40 pati

Fuel Efficiency of Hybrid Cars

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

Impact of Advertising on Product Awareness

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

Impact of Training Programs on Test Scores

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

Medical Test Accuracy and Diagnosis

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

Pre- and Post-Treatment Blood Pressure

A clinical trial is conducted to assess the effectiveness of a new treatment for lowering blood pres

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

Quality Control in Production

A company tests the tensile strength of its products. A random sample of 12 items shows a sample mea

Quality Control: Machine Calibration

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

Reaction Time Testing Under Caffeine Effects

A study examines the effect of caffeine on human reaction times. Two independent random samples of 2

Response Time in a Virtual Reality Task

A technology company is testing a new virtual reality (VR) system for gaming. They measure the respo

Social Media Usage Before and After an Intervention

A researcher studies the effect of a digital detox program on daily hours spent on social media. For

Study Hours and Test Scores

A teacher implements a new study method to improve student performance. Eight students are tested be

Study Hours and Test Scores Regression Analysis

The scatterplot below displays data on college students' study hours (x-axis) and their correspondin

Weight Reduction Program Evaluation

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

Academic Majors and Study Habits

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

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

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

Comparing Exhibition Attendance Among Different Museums

Three museums host the same exhibition and record attendance in three categories: High, Medium, and

Consumer Preference for Advertisement Types

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

Customer Response to Advertising: Chi-Square Test for Independence

A company’s advertising campaign is evaluated by surveying customers on their response (Positive, Ne

Customer Satisfaction Across Store Branches: Homogeneity Test

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

Customer Satisfaction Ratings Across Service Centers

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

Die Fairness: Goodness-of-Fit Test

A six-sided die was rolled 120 times with the following observed frequencies: Face 1: 10, Face 2: 20

Drug Efficacy Across Regions: Homogeneity Test

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

Drug Side Effects Analysis: Chi-Square Test for Independence

In a controlled clinical trial, researchers are investigating whether the frequency of certain side

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

FRQ 9: Student Enrollment Preferences Across Tracks

A high school offers four different tracks: STEM, Humanities, Arts, and Vocational. The school expec

FRQ 19: Comparing Library Usage Patterns Among Departments

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

FRQ 20: Investigative Task - Evaluating the Effectiveness of a Public Health Intervention

A public health department implemented an intensive smoking cessation program aimed at reducing resp

Genetic Ratios in Plant Breeding – Chi-Square Goodness-of-Fit

In a plant breeding experiment, a dominant-recessive trait is expected to follow a 3:1 phenotypic ra

Genetic Trait Distribution Goodness-of-Fit

In a genetic cross the expected phenotypic ratio for a trait is 3:1 (dominant: recessive). A botanis

Genetics Research: Rat Coat Colors

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

Independence Test: Dietary Supplements and Energy Levels

A fitness center surveyed 250 members about their use of dietary supplements (Yes/No) and their self

Insurance Claim Types: Independence Test Across Age Groups

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

Library Membership and Age

A library survey examines whether there is an association between age group and type of membership (

Market Research: Chi-Square Test for Homogeneity of Brand Choices

A market researcher wishes to determine whether consumer brand preference is consistent across three

Patient Outcomes by Treatment: Chi-Square Test for Independence

In a hospital trial, patients are assigned to one of two treatments (Medication A and Medication B)

Product Preference Independence Test by Gender

A survey of 200 participants gathered data on product preference among four options (Product A, B, C

Public Opinion on Policy: Chi-Square Test for Independence

A poll surveyed 600 individuals regarding their stance (Support or Oppose) on a new public policy, a

Quality Control in Manufacturing

A factory produces items that are classified into three quality classes: Class I, II, and III. The p

Simulating the Distribution of the Chi-Square Statistic

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

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

Voting Behavior and Demographics

A survey collected responses from 700 voters regarding their political affiliation (Democrat, Republ

Voting Methods: Chi-Square Goodness-of-Fit

In a local election, voters could choose from three voting methods: In-person, Mail-in, and Online.

Workplace Safety Compliance

A company records the safety compliance of employees in two departments: Manufacturing and Administr

Advertising Data: Predicting Sales

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

Advertising Impact on Sales

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

Advertising Reach and Customer Acquisition

A digital marketing analyst studies the relationship between the number of advertising impressions (

Air Quality and Traffic Flow

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

Automobile Fuel Efficiency

A study analyzes the effect of engine displacement (in liters) on fuel efficiency (measured in miles

Biking Speed and Heart Rate

A sports scientist is investigating the relationship between average biking speed (in mph) during ex

Car Age and Resale Value

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

Car Mileage and Tire Pressure

A car manufacturer wants to study the effect of tire pressure (x, in psi) on car mileage (y, in mile

Clinical Trial Dosage-Response Simulation

A medical researcher investigates the relationship between the dosage of a new medication (in mg) an

Daily Study Hours and GPA

Researchers are interested in analyzing the relationship between the number of hours students study

Dosage-Response in Drug Trials Simulation

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

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 Time on Test Scores

A teacher collects data on the number of hours studied (x) and exam scores (y) out of 100 for 25 stu

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

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

Evaluating the Impact of Work Experience on Promotion Rate

An organizational study examines whether years of work experience (x) affect the promotion rate (y,

Exercise Frequency and Resting Heart Rate

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

Fish Population and Pollution Levels

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

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 Workout Hours on Body Fat Percentage

A fitness study collected data on the number of hours individuals work out per week (x) and their bo

Industrial Emissions and Air Quality

A governmental agency is evaluating the impact of industrial emissions (x, in tons per day) on local

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

Machine Calibration and Defect Rate

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

Mobile App Usage Study

A study examines the relationship between time spent on a mobile app (in minutes) and user satisfact

Plant Growth vs Fertilizer Amount

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

Rainfall and Crop Yield

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

Relationship Between Hours Studied and Test Scores

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

Social Media Use and Academic Performance

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

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

Temperature Effects on Motor Speed

An engineer investigates the effect of ambient temperature ($$x$$, in $$^\circ C$$) on motor speed (

Weekly Hours Worked and Job Productivity

A manufacturing plant studied the relationship between weekly hours worked (x) and job productivity