AP Statistics FRQ Room

AP Class Enrollment Analysis

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

BMI and Blood Pressure Regression Analysis

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

Bus Scheduling and Commuter Wait Times

A city transit authority is investigating whether optimizing bus schedules can reduce average commut

Car Fuel Efficiency Test

A study measures the fuel efficiency of a sample of 50 cars. The sample has a mean miles per gallon

Digital Flashcards vs. Traditional Study for Vocabulary Improvement

A study is conducted to compare the effectiveness of a digital flashcards app versus traditional pap

Dotplot Representation of Home Run Distances

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

Effect of Fertilizer Types on Tomato Yield

An agricultural experiment is designed to test whether different types of fertilizer affect tomato y

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

Event Attendance by Invitation Type

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

Favorite School Lunch Choices

A survey was administered to 500 students about their favorite school lunch option. The partial data

Home Run Distance Analysis

A study measured the distances (in feet) of home runs at 13 ballparks using the following data set:

Home Run Distances Analysis

Consider the following set of home run distances (in feet) measured at 13 ballparks: $$\{387, 400,

Interface Redesign and User Engagement

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

Movie Theater Attendance

Ticket sales at a movie theater are assumed to be normally distributed with a mean of $$150$$ seats

Nature Exposure and Mood Improvement

An environmental psychology study is designed to assess whether guided nature walks improve mood amo

Online Course Satisfaction Hypothesis Test

A university is evaluating the satisfaction level with its online course. In a survey of 200 randoml

Political Polling: Candidate Preference

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

Product Return Rates Across Regions

A company tracks product returns across four regions (North, South, East, West) with outcomes 'Retur

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 and Confidence Interval Implications for Household Incomes

A sociologist is studying household incomes, which are right-skewed. The sociologist uses a simulati

School Survey on Categorical Preferences

A high school conducted a survey of 400 students regarding their preferred school day length. The re

School Year Length Preference Survey Analysis

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

Stem-and-Leaf Analysis of Ages

A stem-and-leaf plot displays the ages (in years) of participants in a study as follows: 2 | 1 3 5

Stemplot Construction: Analyzing a Data Set

A dataset of 11 numbers is provided as follows: {12, 15, 15, 17, 17, 18, 20, 22, 22, 23, 25}.

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 Campaign and Sales Analysis

A company tracked the number of social media impressions (in thousands, x) and corresponding product

Analyzing a Survey on Social Media Use and Sleep

A researcher surveys 100 college students to study the relationship between the number of hours spen

Art Exposure and Creativity Scores

A survey of 40 art students collected data on the number of hours per week they attend art exhibits

Car Crash Safety Feature Evaluation

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

Clinic Survey on Treatment Outcomes

A clinical trial was conducted to evaluate treatment effectiveness. Two treatment protocols were adm

Coffee Shop Sales Analysis

A local coffee shop has recorded data on daily advertising expenditure (in dollars) and the correspo

Complex Survey Analysis: Income and Expenditure Patterns

A national survey collects data on household income (in US dollars) and monthly expenditure (in US d

Correlation vs. Causation Discussion

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

Customer Satisfaction and Purchase Frequency

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

Customer Satisfaction Comparison at Two Store Branches

A retail company collected customer satisfaction data from two store branches, Branch A and Branch B

Customer Satisfaction Survey

A retail store surveyed customers regarding their visit frequency (Frequent vs. Infrequent) and over

Customer Satisfaction: Online vs In-store Shopping

A retail company surveyed its customers about their satisfaction with online versus in-store shoppin

Effectiveness of a Fitness Program

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

Employment Rates of College Graduates

A survey was conducted to compare the employment outcomes of graduates from two colleges. College X

Environmental Awareness Survey

A survey was conducted to explore the relationship between recycling habits and environmental concer

Exploring Temperature and Ice Cream Sales

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

Exploring the Sampling Distribution of the Regression Slope Under Increasing Error Variability

In a study of the relationship between income (x) and expenditure (y), researchers use simulation to

Free Throw Performance in Basketball

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

Housing Prices and Home Size

A study of 40 houses produced the regression equation $$\hat{y}=50+0.15x$$ predicting house price (i

Impact of Caffeine Intake on Reaction Time

In a laboratory study, researchers measured participants' reaction times (in seconds) after ingestin

Inference on the Slope of Study Hours vs. Exam Score

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

Least Squares Regression for Predicting House Prices

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

Neighborhood Safety Survey

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

Nonparametric Alternatives to Linear Regression

Sometimes the assumptions of linear regression (such as linearity and homoscedasticity) are violated

Online Course Engagement and Performance

In an online course, data were collected from 40 students on the number of forum posts (x) and final

Political Polling: Approval Ratings

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

Quality Control in a Bakery

A bakery finds that historically 2% of its cookies are too hard. In a sample of $$100$$ cookies, let

Quality Control in Manufacturing

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

Recycling Attitudes Contingency Table Analysis

A survey of 200 community members was conducted to examine the relationship between recycling behavi

Restaurant Tip Analysis

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

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

Social Media Engagement Study

A social media analyst is comparing the level of high engagement on two platforms. The data collecte

Social Media Use and Academic Performance

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

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,

Study Habits and Exam Pass Rates

A researcher compared exam pass rates between two groups of students enrolled in different study pro

Temperature and Ice Cream Sales

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

Using Residual Plots to Assess Fit in Advertising and Sales Data

A company collects data on its weekly advertising budget (in $1000s, x) and weekly sales revenue (in

Warehouse Shipping Times

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

Academic Performance: Hours Studied and Test Scores

In a high school, a teacher investigates the relationship between the number of hours students study

Analysis of Product Return Rates: Online vs. In-Store

A retailer wants to compare product return rates between online and in-store purchases. Among online

Analyzing a Charity Fundraising Event

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

Assessing Nonresponse Bias in Telephone Surveys

During a telephone survey on community health, only 40% of the contacted individuals respond. Answer

Assessing Sampling Techniques in Market Research for a New Product

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

Assessing Systematic Sampling in a Household Survey

A market research firm wants to survey household expenditures and decides to use systematic sampling

Bootstrapping the Sampling Distribution of a Mean

A researcher has collected exam scores from 15 students and wishes to estimate the sampling distribu

Comparing Two Sample Means in Drug Recovery

A study compares recovery times (in days) of patients treated with two different drugs. Drug A was g

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

Effect of Diet on Cholesterol Levels

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

Evaluating Survey Question Wording Bias

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

Firearm Safety Course Outcomes in Different Regions

A study examined the outcomes of a firearm safety course in two regions. In Region X, 160 out of 200

Hypergeometric Distribution in Quality Inspection

In a batch of 200 items, 10 are known to be defective. A quality inspector randomly selects 20 items

Impact of Advertising on Product Purchase

A company conducted a study on the effect of different advertisement types (Online, TV, Print) on pr

Manufacturing Processes and Product Lifespan

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

Observational Study Versus Experiment in Healthcare

A hospital wants to study the impact of a new dietary program on diabetic patients’ blood glucose le

Simulating Cluster Sampling and its Effects on the Sampling Distribution

A health survey is conducted using cluster sampling by selecting several schools from a district and

Simulating Sampling Distributions for Quality Control in Manufacturing

A manufacturing company produces items that are expected to weigh $$500 \text{ g}$$ on average with

Simulating the Sampling Distribution from a Skewed Distribution

A fast food restaurant is interested in the waiting times (in minutes) of its customers, which are p

Simulation of the Sampling Distribution of Proportions in Quality Testing

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

Systematic Sampling Implementation

A researcher intends to select 150 students from a high school of 1500 students using systematic sam

BMI and Systolic Blood Pressure Regression Analysis

A study investigating the relationship between Body Mass Index (BMI) and systolic blood pressure (in

Campus Computer Virus Spread: Multistage Probability Calculation

On a university campus, computers run on three different operating systems: Windows (60%), Apple (30

Casino Free Chips: Pooling Strategies

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

Comparing Bank Loan Approval Rates

A bank uses two different underwriting policies. Under Policy A, 300 out of 500 applicants are appro

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

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

Comparing Patient Wait Times at Two Clinics

Two clinics recorded patient wait times. Clinic 1 (n = 40) had an average wait time of 25 minutes wi

Cumulative Probability Distribution in AP Exam Scores

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

Customer Satisfaction Survey

A retail company conducted a customer satisfaction survey both online and in-store. The results are

Daily Commute Times: Probability and Expected Value

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

Effect of Fertilizer Type on Plant Growth

An agricultural researcher is studying the effects of three different fertilizer types on plant grow

Effects of Outliers on Sampling Distributions

A simulation study involves drawing samples from a dataset that contains outliers. For each sample,

Exam Score Cumulative Distribution

The following table displays the distribution of scores on an exam from 200 students:

Highway Worker Productivity

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

Household Income and Entertainment Expenditure Regression Analysis

A survey of households examines the relationship between monthly income (in dollars) and monthly spe

Impact of Meditation on Stress Reduction

A mental health clinic is studying whether an 8‐week meditation program reduces stress levels in its

Investigative Study on Public Health Intervention

A local government is assessing the effectiveness of a new public health campaign aimed at reducing

Medication Dosage and Recovery Time Regression Analysis

A clinical study investigates the effect of medication dosage (in mg) on patient recovery time (in d

Multi-center Clinical Trial for a New Vaccine

A large-scale clinical trial is conducted across several hospitals to evaluate the efficacy of a new

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

Online Advertisement Click-Through

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

Rare Defects and Poisson Approximation

A factory produces electronic components with a defect rate of 0.002. In a shipment of 2000 units, l

Reading Preferences by Genre and Format

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

Restaurant Tip Percentage Analysis

A restaurant manager claims that the average tip percentage is 18%. To test this claim, a random sam

Simulated Coin Toss Sampling Distribution

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

Simulating Clinical Trial Successes

A new drug has a success probability of 0.65. In a clinical trial, 30 patients are treated independe

Simulating the Expected Value in a Lottery Game

Consider a lottery game with payouts given by the following probabilities: $$P(\$2)=0.5$$, $$P(\$5)=

Software Use in Organizations

A survey of 230 organizations recorded the primary operating system used in different departments. T

Suit Name Letter Count

A card is drawn from a standard 52-card deck. Let the random variable $$X$$ be the number of letters

Tip Amounts from Different Meal Services

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

Understanding the Central Limit Theorem through Simulation

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

Urban Traffic Volume and Air Quality Regression Analysis

A city planner studies the relationship between daily traffic volume (in thousands of vehicles) and

Analysis of Athletic Performance Improvements

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

Battery Life Analysis Using Normal Distribution

A battery manufacturer claims that the lifespan of its batteries is normally distributed with mean $

Caffeine Content Analysis

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

Central Limit Theorem in Quality Control

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

Comparing Average Temperatures in Two Cities

City A has an average temperature of 70°F with a standard deviation of 5°F based on a sample of 50 d

Comparing Pass Rates Between Two Schools

Two high schools are comparing their students' pass rates on a standardized test. School A had 200 s

Customer Complaints by Service Type

A telecommunications company recorded customer complaints for two types of services: Phone Service a

Differences in Genetic Mutations by Age

A study investigates the number of genetic mutations contributed by fathers of different ages. For 4

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

Employment Benefits Perception

A company surveyed its employees regarding their perception of employment benefits. The responses ar

Estimator Bias: Maximum vs. Mean in Soccer Scores

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

Evaluating 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

Lightbulb Life Expectancy Analysis

A particular brand of lightbulb has a lifespan that is approximately normally distributed with a mea

Quality Control in Baseball Production

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

Sample Proportion Variability in Customer Preference Studies

Two separate studies examine customer preference for a new product. Study 1 finds 60% preference in

Sampling Distribution for Differences in Sample Proportions in Political Polling

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

Sampling Distribution for Sample Proportions: Political Polling

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

Social Media Engagement Proportions

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

Social Media Use and Sleep Duration

Researchers investigated the impact of social media use on sleep duration. Two independent groups we

Survey on Learning App Preference

In a high school, it is believed that $$65\%$$ of students prefer using a new learning app. A random

Advertising Impact on Brand Recognition

A company runs a new advertisement in two regions. In Region 1, 210 out of 350 respondents recognize

Comparative Study on Voter Registration Between Two States

Two neighboring states conducted surveys on voter registration. In State A, 320 out of 400 eligible

Comparing Participation Rates in Exercise Programs Across Cities

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

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 a Population Proportion

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

Confidence Interval for Proportion in Market Research

A market research firm surveys 500 consumers and finds that 265 like a new product.

Consumer Preference: Hypothesis Testing for a Single Proportion

A company claims that at least 40% of consumers prefer its new product. In a sample of 250 consumers

Consumer Product Hypothesis Test

A company claims that at least 60% of its customers like a new product. To test this claim, a simple

Customer Preference Difference Between Cities

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

Educational Assessment: Confidence Interval for Passing Rate

A school administered a standardized test to 800 students, and 560 of them passed. Answer the follow

Employee Burnout Study

A company conducted a survey to assess employee burnout. In a simple random sample of 250 employees,

Employee Retention in a Tech Firm

A tech company wants to analyze its employee retention rate. Out of a random sample of 200 employees

Environmental Awareness Survey

A survey was conducted to assess the proportion of residents aware of local recycling programs. In a

Epidemiology Study: Difference in Disease Incidence

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

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

Evaluating Public Support for a Tax

A poll was conducted to measure public support for a proposed tax. In the first survey, 1000 voters

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

Gender Differences in Product Preference

A market survey was conducted to measure interest in a new gadget. A sample of 400 males showed that

Hypothesis Testing for Brand Satisfaction

A company claims that 85% of its consumers are satisfied with its product. A random survey of 200 cu

Interpreting a Confidence Interval for Hybrid Learning Preference

At a high school, a survey of 100 students reveals that 40 prefer a hybrid learning model.

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

Nutrition Labeling Impact Study

A government agency implements a policy requiring prominent nutritional labels on packaged foods. A

One-Sided Election Polling Analysis

In a survey of 600 likely voters, 330 support a particular candidate. The candidate’s campaign claim

Online Advertising Impact Study

An online retailer wishes to study whether exposure to a particular digital advertisement increases

Planning a Comparative Survey

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

Political Polling: Candidate Approval

Two independent polls were conducted to assess approval ratings for a political candidate. Poll 1, s

Product Defect Rates in Manufacturing

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

Public Health Confidence Interval

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

Public Library Usage Survey

A city council conducted a survey to determine the proportion of residents using the public library.

Public Transit Usage

A city planning study compares the proportion of residents using public transit in two cities. City

Restaurant Hygiene Survey Analysis

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

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

Sampling Distribution and Confidence Intervals for Proportions

A researcher is studying the proportion of households with internet access. In a simple random sampl

School Intervention Study

A school implements a new intervention aimed at increasing the proportion of students passing a stan

Service Reliability Study Analysis

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

Social Media Usage Among Age Groups

A survey on social media usage was conducted among two age groups. Among individuals under 30, 160 o

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

Web Advertisement Click-Through Rates

An online marketing team is comparing the click-through rates of two advertisements. Ad A was shown

Accident Rates Comparison Between Departments

A study was conducted over 20 months in two departments of an assembly plant to compare accident rat

Assessing a New Teaching Method

A study compares two teaching methods to assess their impact on student performance. In a randomized

Average Household Electricity Usage

An energy study reports that for a random sample of 40 households, the average monthly electricity u

BMI and Systolic Blood Pressure Analysis

The scatterplot below shows data on body mass index (BMI, x-axis) and systolic blood pressure in mmH

Coffee Consumption and Alertness Scores

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

Comparative Analysis of Blood Pressure Between Population Groups

Public health officials are comparing systolic blood pressure levels between an urban population and

Comparing 3-Point Percentage Rates

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

Comparing Manufacturing Processes

A company uses two different processes to manufacture a particular part. Process X is evaluated on a

Effect of a New Fertilizer on Crop Yield

An agricultural researcher investigates the effect of a new fertilizer on the yield of a particular

Energy Consumption Analysis

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

Investigating Student Reaction Times

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

Life Span Analysis of Light Bulbs

A manufacturer claims that its light bulbs have a long lifespan. In a quality test of 15 randomly se

Lifespan of New Light Bulbs

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

Plant Growth under Different Fertilizers

A botanist is studying the effect of a new fertilizer on plant growth. A random sample of 12 plants

Pre- and Post-Treatment Blood Pressure

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

Pre-Test and Post-Test Scores Analysis

The scatterplot below represents data on students' pre-test scores (x-axis) and post-test scores (y-

Reaction Time One-Sample t-Test

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

Simulation of Sampling Distribution with Measurement Error

A lab is troubleshooting a sensor that measures the weight of produced components. A simulation is c

Temperature and Water Consumption Analysis

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

Weight Loss Study Confidence Interval

A nutritionist is studying the effect of a new diet on weight loss. A random sample of 16 subjects y

Wind Speed Measurements: Station Upgrade Impact

A weather station upgrades its sensors and collects paired wind speed measurements from before and a

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.

Book Genre Popularity Study

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

College Major vs Gender: Chi-Square Test for Independence

A college survey recorded the number of students by major (Science, Humanities, Business, Arts) and

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

Computer Usage and Major Association Independence Test

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

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

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

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

Examining Political Ideology: Chi-Square Test for Homogeneity

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

Fair Dice Rolling Goodness-of-Fit Test

A die is believed to be fair. In 120 rolls, the outcomes were observed as follows: Face 1 = 14, Face

FRQ 12: Employee Training Program and Job Promotion

A company is investigating the effectiveness of its training program on job promotions. The collecte

FRQ 13: Customer Loyalty Across Store Branches

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

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

Major Distribution Across Colleges Goodness-of-Fit Test

A university claims that the distribution of student majors is as follows: 25% Sciences, 35% Humanit

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

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

Music Genre Preferences Across Cities – Chi-Square Test for Homogeneity

A market research firm surveyed residents in four different cities (City A, City B, City C, City D)

Quality Control: Defective Items in Production Lines

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

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

Social Media Usage Among Age Groups: Independence Test

A survey of 250 social media users collected data on their primary platform (Facebook, Instagram, Tw

Sporting Event Results: Homogeneity Test

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

Sports Preferences by Gender: Chi-Square Test for Independence

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

Student Course Preference and Major

A university surveys 300 students to determine if course delivery preference (Online vs. In-Person)

Student Enrollment by Gender and Major: Chi-Square Test for Independence

A university is investigating if student major (STEM, Arts, Business) is independent of gender (Male

Traffic Accident Severity

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

Voter Initiative Support Homogeneity Test Across Regions

A study examines voter support for a new initiative in three regions: North, Central, and South. Ind

Workplace Safety Compliance

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

Advertising Budget and Sales Revenue

A marketing analyst is studying the relationship between a company’s monthly advertising budget (in

Advertising Spend and Website Traffic

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

Car Fuel Efficiency and Car Weight Regression Analysis

An automotive engineer analyzes the relationship between a car's weight (in kg) and its fuel efficie

Coffee Consumption and Alertness

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

Coffee Consumption and Alertness Score

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

Crop Yield and Fertilizer Application

An agronomist is examining how the amount of fertilizer applied (x, in kg) affects crop yield (y, in

Dosage-Response in Drug Trials Simulation

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

Exercise Duration and Weight Loss

A fitness study explores the relationship between exercise duration (in minutes) and weight loss (in

Exercise Duration vs Heart Rate

A fitness researcher analyzed the relationship between exercise duration (in minutes) and heart rate

Fish Population and Pollution Levels

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

Fuel Efficiency and Car Weight

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

House Prices and Square Footage

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

Impact of Teaching Methods on Math Performance

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

Library Study Rooms Reservation vs Exam Success

A university service collected data on the number of library study room reservations made by student

Machine Runtime and Maintenance Costs

An operations manager is investigating whether the total runtime of an industrial machine (in hours

Marketing Campaign Effectiveness Simulation

A marketing analyst is examining the relationship between advertising spending (in dollars) and sale

Medical Dosage and Blood Pressure Reduction

A clinical study examines the effect of a new drug dosage (x, in mg) on the reduction of blood press

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

Student Performance and Attendance

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

Study Hours and SAT Scores: Private vs Public

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

Study Program Length and Post-Graduate Salary

A career advisor is studying whether the length of graduate programs (in years) is related to the me

Traffic Volume and Pollution Levels

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

Urban vs Rural Pollution Levels

An environmental study examined the relationship between daily traffic volume (in thousands of vehic

Water pH and Aquatic Life Diversity

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