AP Statistics FRQ Room

Analyzing a Stem-and-Leaf Plot of Weights

A stem-and-leaf plot displays the weights (in kg) of 40 participants in a fitness program as follows

Analyzing z-Scores from a Frequency Distribution

The following table displays z-scores along with their corresponding cumulative percentile rankings

College Admissions Test Scores

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

Comparing Cumulative Frequency Graphs for Age Distributions

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

Comparing Exam Score Distributions

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

Comparing Sleep Hours: High School vs College

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

Delivery Time Hypothesis Test

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

Effect of Skewness on the Sampling Distribution of the Mean

A company tracks daily website visits which are heavily right-skewed. A data analyst simulates drawi

Home Run Distances: Mean, Median, and Outlier Impact

A dataset of home run distances (in feet) recorded in 13 ballparks is given as follows: {387, 400, 4

Impact of Incentives on Survey Participation

A market survey was carried out with two groups: one received an incentive and the other did not. In

Impact of Transformations on Data

Consider the following dataset representing test scores: {70, 80, 85, 90, 100}. Answer the followin

Investigative Analysis of Public Health Survey on COVID-19

A public health survey was conducted with 500 adults to assess COVID-19 vaccination status, experien

Investigative Task: Evaluating a School Breakfast Program

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

Matching Data Sets and Estimating Percentiles

A cumulative frequency table for exam scores of 100 students is provided below: | Score | Cumulativ

Political Affiliation and Media Consumption

A study surveyed 300 voters on their political affiliation (Party A, Party B, Independent) and their

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

Sleep Deprivation and Reaction Times

A behavioral study is designed to examine the effect of sleep deprivation on reaction times. Partici

Student Major and Internship Status

A study of 200 college students recorded their major (STEM or Non-STEM) and internship status (Had I

Weekly Exercise Sessions

Assume that on any given day, a person exercises for at least 30 minutes with a probability of $$0.4

Analyzing Social Media Usage and Self-Esteem

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

Attendance and Test Performance

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

Call Duration Analysis in a Service Center

In a call center, call durations (in minutes) are normally distributed with a mean of $$3$$ minutes

Car Crash Safety Feature Evaluation

An automotive safety engineer evaluates two car models based on their performance in crash tests. Th

College Major by Gender

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

Comparing Marginal and Conditional Distributions in a Two-Way Table

A car dealership survey recorded data on car color and type. The dealership is interested in the dis

Comparing Two Regression Models for Chlorophyll Content Prediction

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

Correlation vs. Causation Discussion

A study finds a high positive correlation between ice cream consumption and the number of drowning i

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

Daily Screen Time and Sleep Quality

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

Effectiveness of a Fitness Program

A fitness center is evaluating the effect of a new training program on clients' ability to meet thei

Elderly Health Program Evaluation

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

Email Marketing Response Rates

A company ran two email marketing campaigns and recorded the number of recipients who responded and

Environmental Study: Temperature and Ice Cream Sales

An environmental study tracked ice cream sales (in hundreds of dollars) and the daily high temperatu

Evaluating Coefficient of Determination in Athletic Performance

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

Experience and Salary: Exploring a Nonlinear Relationship

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

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

Manufacturing Defects in Two Production Lines

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

Online Learning Preferences

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

Predicting Apartment Rents

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

Predicting Student Exam Scores from Study Hours

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

Quality Control in Manufacturing

A factory produces light bulbs and historically 5% of bulbs are defective. A quality control inspect

Residual Analysis and Outlier Detection in a Weight Loss Study

A weight loss program is evaluated by predicting weight loss (in pounds) using a regression model ba

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 Mean Residuals in a Regression Model

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

Smartphone Brand Loyalty

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

Social Media Activity and Face-to-Face Interactions

In a survey of 40 individuals, data were collected on the number of social media posts per week (x)

Sports Performance: Height vs. Weight Analysis

A sports analyst collected data on the heights (in inches) and weights (in pounds) of athletes. The

Study Habits and Exam Scores: Regression Inference

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

Temperature and Ice Cream Sales

A study over 30 days recorded the average daily temperature (in °F) and corresponding ice cream sale

Wait Time and Meal Satisfaction

A restaurant collected data from 40 customers on their wait time (in minutes) and meal satisfaction

Warehouse Shipping Times

Shipping times from a warehouse are normally distributed with a mean of $$4.5$$ days and a standard

Analysis of Boxplots from an Experiment on Pulse Rates

Researchers conducted an experiment comparing the effects of three beverages (coffee, caffeinated co

Community Fitness Program and Weight Loss

A local government launches a community fitness program to help residents lose weight. The program i

Commute Time and Job Satisfaction

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

Customer Satisfaction with New vs. Old Product

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

Designing a Prospective Study for Teaching Methods

A school district wants to study the effect of a new teaching method on student performance on stand

Designing a Randomized Controlled Trial for a New Drug

A pharmaceutical company is preparing to test the efficacy of a new drug intended to lower blood pre

Designing a Representative Student Survey

A university desires to survey its 10,000 students about campus dining experiences. To ensure repres

Designing a Stratified Random Sample for Student Opinions on Distance Learning

A researcher intends to survey high school students' opinions on the transition to distance learning

E-Commerce Website Redesign and Consumer Behavior

An online retailer has redesigned its website and wants to assess whether the change has affected co

Effect of Population Variability on the Sampling Distribution

A simulation study is conducted drawing samples of size $$n = 30$$ from populations with the same me

Evaluating a New Teaching Method

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

Evaluating Survey Question Wording Bias

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

Evaluating Survey Sampling Methods

A researcher conducts an online voluntary response survey to measure public opinion on a new policy.

Evaluating the Effect of Exercise on Blood Pressure Reduction

A study measured the reduction in blood pressure in two groups over a 6‐month period. Group 1 (Exerc

Evaluation of Experimental Design and Inference in Consumer Behavior Studies

A market research study investigates the effect of different advertising strategies on consumer purc

Exercise Frequency and Cholesterol Levels

A study investigates the relationship between the number of hours of exercise per week (x) and total

Experimental Design: Evaluating a Review Course for SAT Scores

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

Impact of Advertising on Sales Revenue

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

Impact of Sample Size on Confidence Interval Width

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

Investigating Effects of Population Variability on Sampling Distributions

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

Investigating Response Time in Emergency Calls

A retrospective study collected data on the response times (in minutes) of emergency services from 6

Public Health Intervention on Smoking Cessation

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

Replication in Experimental Designs: Water Purification Study

Researchers are testing various water purification techniques in an experimental study. Replication

Sampling Distribution in Voter Polling

A polling organization is estimating the approval rating for a political candidate. Suppose the true

School Lunch Programs and Student Health

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

Simulation Study on the Distribution of the Sample Range

A researcher is studying the spread of values in a uniformly distributed population on the interval

Smartphone Usage and Sleep Quality

Examine the relationship between smartphone usage and sleep quality among college students. Research

Systematic Sampling in a Voter Preference Survey

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

Voting Preference Analysis

A political analyst collected data on voting preferences by age group. The table below shows the num

Comparing Customer Satisfaction in Two Coffee Shops

A survey was conducted to compare customer satisfaction between two coffee shops. The table below su

Comparing Simulation Results for Rainy Days

A simulation study recorded weather in two cities over a 30-day month. The results are as follows:

Cumulative Probability Distribution in AP Exam Scores

The following table shows the distribution of scores on an AP exam: | Score | Frequency | |-------|

Daily Commute Times: Probability and Expected Value

A local survey provides the following probability distribution for daily commute times (in minutes):

Effects of Noise Levels on Worker Productivity

A company is investigating whether ambient noise in the workplace affects employee productivity. Emp

Employee Training and Department Performance

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

Genetics: Inheritance Probabilities

In a certain plant species, each seed has a 75% probability of inheriting a dominant allele, indepen

High School SAT Scores Analysis

A school district collected SAT scores from a random sample of 60 students. The sample mean is $$\ba

Highway Worker Productivity

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

Hospital ER Wait Times

A hospital is interested in assessing the average wait time in its emergency room. In a random sampl

Machine Failures in a Factory: A Binomial Approach

In a factory setting, each machine fails with a probability of $$0.05$$ on a given day, independentl

Manufacturing Process Downtime

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

Medical Treatment Recovery Rates Comparison

A clinical trial compared two treatments for a particular medical condition. Treatment A was adminis

Mobile App vs. Printed Pamphlet for Increasing Exercise Duration

A public health organization wants to determine whether a mobile app intervention or a printed pamph

Multistage Probability: Virus Infection on Campus Computers

On a university campus, 60% of computers run Windows, 30% run Apple, and 10% run Linux. A virus affe

Quality Control in Manufacturing

A factory produces items with a defect probability of $$0.05$$ per item. Items are produced in batch

Sampling Distribution from a Triangular Population

A simulation is performed where samples are drawn from a triangular distribution defined on the inte

Simulation Analysis of Measurement Process Reliability

In a laboratory setting, a measurement instrument with known error characteristics is used to record

Standardized Test Strategies and Scores

A standardized test administered to 800 students records the strategy used when unsure of an answer.

Startup Daily Profit Analysis

A startup estimates its daily profit with the following outcomes: a loss of $$200$$ dollars (probabi

Student Study Hours and Exam Performance Regression Analysis

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

Testing a New App Feature through A/B Testing

A tech company is conducting an A/B test to evaluate a new feature that is intended to enhance user

Transformation of Payout Values

A game machine produces a random payout $$X$$ with a mean of $5 and a standard deviation of $3. A re

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 =

University Exit Exam Pass Rate

A local university advertises that at least 70% of its students pass the exit exam. In a random samp

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 Server Demand Modeling

Historical data for a website shows that the daily number of server requests (in thousands) follows

Analyzing Differences in Means Between Two Machines

Two machines produce metal rods. Machine A produces rods with a mean length of $$20$$ cm and a stand

Assessing Estimators in Quality Testing

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

Battery Lifespan Analysis

A company produces batteries whose lifespans (in hours) are normally distributed with $$\mu = 500$$

Blood Pressure Reduction Study

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

College Major and Internship Experience

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

Comparing Class Test Scores

Two independent classes took a standardized test. Class X (with $$n=30$$) had a mean score of 78 wit

Comparing Juice Bottling Process

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

Environmental Concerns by Community Type

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

Evaluating Estimators for Baseball Weight

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

Financial Returns: Biased vs. Unbiased Estimators

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

High Math Anxiety and Brain Activity

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

Impact of Devices on Online Purchases

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

Music Streaming Service Satisfaction

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

Normal Distribution Calculation: Component Lifespan

A certain machine component has a lifespan that is approximately normally distributed with mean $$\m

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

Polling Data Analysis

In a large election, the true support for a candidate is believed to be $$52\%$$. A random sample of

Quality Control of Production Errors

In a manufacturing facility, the number of production errors per day follows a distribution with a m

Sampling Distribution for Sample Means: Energy Drink Caffeine Levels

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

Simulated Daily Sales Distribution

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

Simulating the Sampling Distribution of the Range

A researcher is interested in the range of scores on a standardized test. The population range is kn

Social Media Engagement Proportions

A social media platform reports that 65% of its users engage with sponsored content. A random sample

Stock Returns Probability Calculation

Assume that annual stock returns are normally distributed with a population mean of 8% (0.08) and a

Student Test Scores Sampling Distribution

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

Analysis of Emergency Room Wait Times Satisfaction

A hospital surveyed patients about their satisfaction with emergency room wait times. In a sample of

Assessing Advertising Effectiveness with Proportion Data

An advertising firm claims that its new campaign results in a purchase rate of at least 30%. In an e

College Acceptance Rate Comparison

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

Comparative Analysis of Two Healthcare Clinics

Two healthcare clinics are comparing the success rate of a new treatment. At Clinic 1, 80 out of 100

Comparing Voter Turnout between Two Regions

Two regions conducted independent surveys before an election. In Region A, a random sample of 200 vo

Conservation Program Study

A local government has implemented an environmental conservation program intended to increase the pr

Customer Loyalty Program Impact Study

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

Customer Satisfaction in a Retail Store

A large retail chain conducted a survey to measure customer satisfaction. Out of a simple random sam

Effectiveness of a New Vaccine

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

Epidemiology Study: Difference in Disease Incidence

An epidemiological study examines disease incidence in two groups. In the exposed group (n = 400), t

Evaluating Strike Support

A union conducted a survey among 125 members to decide on whether to support a strike. In the survey

Impact of a New Regulation

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

Marketing Survey: Brand Loyalty Across Regions

A marketing survey compares brand loyalty across two regions. In Region 1, 210 out of 300 respondent

Measuring Customer Preferences

A market survey was conducted on customer preferences for two competing brands. For Brand X, 300 cus

Medical Study: Confidence Interval for Treatment Success

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

Online Advertising Effectiveness

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

Online Education Satisfaction

A study comparing satisfaction with education methods surveyed two groups. One group of online stude

Public Health: Smoking Rates by Region

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

Retail Coupon Usage Among Customers

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

Retail Customer Satisfaction Survey Design

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

Sample Size Determination for Desired Margin of Error

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

School Lunch Program Participation

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

Smoking Cessation Campaign Study

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

Survey Analysis: Confidence Interval for College Students' Online Class Preference

A survey of college students was conducted to estimate the proportion of students who prefer online

Vaccine Hesitancy Survey Design

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

Voter Preferences by Age Group

A recent survey collected data on voter preferences for two political candidates among voters in two

Voting Patterns on Renewable Energy

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

Website A/B Testing

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

Analysis of Weekly Exercise Duration

A wellness program is designed to increase weekly exercise time. In a sample of 16 participants unde

Blood Pressure Reduction Confidence Interval

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

Coffee and Exam Performance

A university study collected data on whether students drink coffee and their exam performance. The t

Coffee Consumption and Alertness Scores

A study investigates whether coffee consumption affects alertness. Two independent samples are consi

Comparing Average Heart Rates in Two Exercise Regimens

A fitness study compared the effects of two different exercise regimens on heart rate. Group 1 (n =

Comparing Two Diet Programs on Weight Loss

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

Customer Satisfaction Survey

A popular online retailer claims an average customer satisfaction rating of 8.5 (on a 10-point scale

Customer Wait Time in Service

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

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

Diet Program Effectiveness

A research study was conducted to compare the effectiveness of two diet programs in achieving weight

Difference in Accident Rates

In a study of safety in a manufacturing plant, monthly accident data were collected for two independ

Effect of Medication on Blood Pressure: Paired Data Analysis

A study was conducted on 30 patients to evaluate the effect of a new medication on systolic blood pr

Effect of Training on Typing Speed: Paired Analysis

A company implemented an intensive typing training program. Typing speeds (in words per minute) were

Effectiveness of a New Teaching Method

A school district wants to evaluate the effectiveness of a new teaching method on student test score

Exam Score Analysis with Unequal Sample Sizes

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

Fertilizer Impact on Plant Growth

An agricultural researcher investigates whether a new fertilizer affects plant growth. Two independe

Income Analysis for a Tech Company

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

Machine Downtime Analysis

A manufacturing plant monitors the daily downtime (in minutes) of a critical machine. Over 40 indepe

Nutritional Study on Caloric Intake

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

Online Platform User Engagement

An online platform wants to compare the average daily time spent by users in two different regions.

Physical Activity and Cholesterol Levels

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

Pre- and Post-Intervention Test Score Analysis

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

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

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

Simulation of Sampling Distribution for Average Calorie Content in Energy Bars

A food quality control manager conducts a simulation study to evaluate the average calorie content o

Sports Performance and Training Regimen

A sports scientist investigates the effect of two training regimens on athletic improvement. Athlete

Temperature and Electricity Consumption Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and electricity consumption in

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

Tennis Serve Speeds

A sports scientist is analyzing the serve speeds (in km/h) of a professional tennis player. A random

Test Score Comparison between Two Classes

Two different classes took a standardized test. Class A (n = 30) had a mean score of 78 with a stand

Test Scores in a New Curriculum

A school implements a new curriculum and collects standardized test scores from a random sample of 2

Workplace Wellness Program Evaluation

A company evaluates its workplace wellness program by comparing the health outcomes of employees who

Age Group and Exercise Habits

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

Bike-Sharing User Gender Distribution Goodness-of-Fit Test

A bike-sharing company claims that the gender distribution of its users is 60% male and 40% female.

Blood Type Distribution: Goodness-of-Fit Test

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

Comparing Preferences for Social Media Platforms Across Age Groups

A survey examines if social media platform preference is associated with age group. The data collect

Consumer Preference for Advertisement Types

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

Customer Complaint Categories – Chi-Square Goodness-of-Fit

A customer service center categorizes complaints into four types: Billing, Technical, Service, and O

Customer Satisfaction Across Regions

A retail chain conducted a survey to assess customer satisfaction in three different regions: North,

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

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

Customer Satisfaction Survey Across Store Locations

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

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

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

Distribution of Housing Types in a City

A city planning department is examining the distribution of housing types in the city. They expect t

Drug Efficacy Across Regions: Homogeneity Test

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

FRQ 4: Quality Control in Manufacturing Defects

A manufacturer claims that defects in its production process are distributed among three types: Type

FRQ 13: Customer Loyalty Across Store Branches

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

FRQ 14: Online Learning Effectiveness Based on Student Feedback

A survey is conducted to determine if the mode of instruction (Online vs. In-person) is associated w

FRQ 16: Association Between Marital Status and Voting Behavior

A study examines whether marital status is associated with voting behavior for Party X versus Party

FRQ 18: Evaluating Distribution of Blood Types in a Sample Population

A hospital expects the distribution of blood types in the general population to be: Type O: 45%, Typ

Goodness-of-Fit for Beverage Preferences

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

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

Participation in Extracurricular Activities: Chi-Square Test for Homogeneity

A school district wants to compare participation rates in extracurricular activities among high scho

Preferred Study Methods: Homogeneity Test Across Colleges

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

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

Satisfaction Survey Among Product Users: Chi-Square Test for Independence

A company wants to investigate whether customer satisfaction is independent of product type. A surve

Shopping Preferences: Homogeneity Test Across Regions

A retail chain surveyed customers in four regions on their preferred shopping mode: In-store or Onli

Simulating the Distribution of the Chi-Square Statistic

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

Smoking and Lung Disease: Independence Test

A survey of 300 individuals reports the following counts: Smoker with lung disease = 40, Smoker with

Sporting Event Results: Homogeneity Test

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

Voter Preferences Among Four Candidates – Chi-Square Goodness-of-Fit

An election poll of 800 voters reports the following counts for four candidates: Candidate A: 220, C

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 Spending and Sales Revenue

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

Air Quality and Traffic Flow

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

Altitude vs Cooking Time

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

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

Coffee Temperature vs Reaction Time

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

Comparing Slopes for Tutoring Effects on Test Score Improvement

A school district evaluates the effect of after-school tutoring on test score improvement for studen

Consumer Spending and Income Levels

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

Daily Steps vs Calorie Burn

A fitness app developer examined the relationship between the number of daily steps and calorie burn

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

Employee Experience and Salary

A human resources study examines the relationship between years of work experience ($$x$$) and annua

Engine Size vs Highway Fuel Efficiency

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

Fish Population and Pollution Levels

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

Fitness Tracker Study: Daily Steps and Weight Change

A fitness study examined whether daily steps (x, in thousands) predict weekly weight change (y, in p

House Price Prediction Simulation

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

Ice Cream Sales and Temperature

A vendor analyzes the relationship between daily average temperature (in °C) and ice cream sales (in

Internet Speed and Streaming Buffer Time

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

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 Recovery Time

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

Mobile App Usage Study

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

Rainfall vs Crop Yield

An agricultural economist is investigating the relationship between annual rainfall (in inches) and

Real Estate Regression Analysis

A real estate analyst collected data on 30 homes to study the relationship between a home's square f

Social Media Influence on Product Sales Simulation

A business analyst wants to understand the effect of time spent on social media advertising (in hour

Weather Forecasting: Humidity vs. Chance of Precipitation

Meteorologists studied the relationship between relative humidity (x, in percentage points) and chan

Weight Loss and Diet Adherence

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