AP Statistics FRQ Room

AP Music Tastes Survey

A survey of 320 students about their favorite music genre produced the following data: | Genre

App Usage: Comparing Two Advertising Campaigns

A mobile app company ran two advertising campaigns. In Campaign 1, 400 out of 800 users clicked the

Beverage Preference in Two Cities

A beverage company surveyed residents from two cities regarding their favorite drink. In City 1, 180

Car Price and Mileage Regression Analysis

A used-car dealership analyzes data from 80 vehicles to predict the selling price (in thousands of d

Distribution of Heights in a Grade

A study on the heights (in centimeters) of students in a particular grade produced the following fre

Effect of Exercise Duration on Heart Rate

A fitness study investigates the effect of exercise duration (in minutes) on a person's heart rate (

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

Effectiveness of a New Drug

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

Effects of Sample Size on the Sampling Distribution in Temperature Data

A meteorologist is studying daily high temperatures in a city over the summer. The temperatures are

Evaluating Marketing Strategies: Online Ad A/B Test

A company performed an A/B test for two versions of an online advertisement to compare their click-t

Home Run Distance Analysis

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

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

Irrigation Techniques and Crop Yield

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

New York City Taxi Mileage Distribution

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

Online Shopping Preference by Age Group

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

Parent Survey on School Length

A survey of 2000 parents asked which school year length they preferred. The following table summariz

Simulated Sampling Distribution of the Standard Deviation

Consider a normal population with $$\mu = 50$$ and $$\sigma = 8$$. A researcher uses simulation to g

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

Survey of Smartphone Usage Time

A survey of 500 students categorized their daily smartphone usage (in hours) with the following data

Survey Response Methods Comparison

A survey was administered using two methods: telephone and online. In the telephone survey, 115 out

Vehicle Type and Fuel Preference

A survey was conducted among 350 respondents regarding their vehicle type (Car, Truck) and fuel pref

Analyzing Curvilinear Relationship and Data Transformation

A botanist records the amount of fertilizer applied (x, in grams) and the resulting plant growth (y,

Assessment of Internet Usage and Academic Performance

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

Contingency Table Analysis: Cuteness Factor Study

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

Effects of Dropping a High-Leverage Observation

A dataset of 12 observations is used to fit a linear regression model predicting a response variable

Evaluating Housing Market Trends Through Transformation

A real estate analyst studies the relationship between house square footage (x) and sale price (y, i

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

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

Fitness Program Enrollment

A local gym evaluated enrollment trends by comparing two program types (Yoga vs. CrossFit) and atten

Interpreting a Simple Linear Regression Model in Advertising

A company studies the relationship between advertising spending (in $1000s) and sales revenue (in $1

Marketing Survey: Advertising Budget vs. New Customers

A marketing survey collected data on weekly advertising budget (x, in thousands of dollars) and the

Medical Test Accuracy and Disease Prevalence

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

Monte Carlo Simulation: Effect of Nonlinearity on Pearson's Correlation

A statistician uses Monte Carlo simulation to explore how nonlinearity in data affects the sampling

Online Course Enrollment Prediction

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

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

Public Health Campaign on Smoking Cessation

A public health department launched a campaign to help individuals quit smoking. A study was conduct

Scatterplot Analysis: Teen Social Media Usage

A study collected data on the number of close friends (X) a group of teens reported and the number o

Simulation Study for Confidence Intervals in Linear Regression Predictions

A marketing analyst uses simulation to assess the performance of confidence intervals in predicting

Social Media Use and Online Privacy

In a study on digital behavior, participants were surveyed about their level of social media usage (

Sports Performance and Training Type

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

Temperature and Ice Cream Sales

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

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

Bias in Random Digit Sampling

A researcher uses random digit dialing to contact households for a survey. However, certain demograp

Comparing Sampling Variability Across Methods

A study to estimate the mean age of teachers uses four different sampling methods. Ten samples are t

Comparing Stratified and Cluster Sampling Methods in a Health Survey

A public health researcher is designing a survey to assess attitudes toward vaccination in a multi-n

Consumer Preferences for Coffee Types

A survey was conducted in a city to understand coffee type preferences among residents from differen

Customer Satisfaction and Purchase Frequency: An Inference Study

A retail company surveys its customers regarding their satisfaction rating (on a 1–5 scale) and the

Customer Satisfaction Proportion Sampling

A company has found that 80% of its customers are satisfied with its service. A survey is conducted

Data Collection in a Prospective Observational Study

A hospital conducts a prospective study to evaluate recovery times following a specific surgical pro

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 Sampling Plan for College Demographics

A university wants to estimate the average GPA for all its students. Given that the student populati

Effect of Diet on Cholesterol Levels

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

Efficacy of a Mobile App for Tracking Physical Activity

A study compared the effectiveness of a mobile app in helping users meet their daily step goals. In

Energy Conservation Campaign and Household Energy Use

A municipal government conducted an energy conservation campaign aimed at reducing household energy

Evaluating Survey Question Wording Bias

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

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

Interpreting a Scatterplot from a Survey on Sleep and Test Scores

A study surveys high school students regarding their average nightly sleep (in hours) and their most

Interpreting Observational Study Data on Exercise and Blood Pressure

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

Investigating Effects of Population Variability on Sampling Distributions

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

Investigating Voluntary Response Survey Bias

A mid-sized university is conducting an online survey about campus safety. The survey is distributed

Matched Pairs Design in Educational Research

A school district is evaluating two teaching methods by having the same students experience both met

Online vs. In-Person Shopping Preferences

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

Predicting Car Mileage from Engine Size

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

Retrospective Study Analysis on a Health Outbreak

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Sampling Methods in a Stratified Design

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

Simulation of the Law of Large Numbers

A classic coin-flipping experiment is simulated to illustrate the Law of Large Numbers. In the simul

Simulation of the Sampling Distribution of the Sample Variance

A researcher runs a simulation to approximate the sampling distribution of the sample variance from

Smoking Impact on Lung Capacity: Regression Study

Researchers are investigating the relationship between the number of years a person has smoked (x) a

Social Media Usage among Teenagers

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

Sports Performance Data Analysis

A coach collects sprint time data (in seconds) from a convenience sample of 30 athletes during pract

Survey on Public Opinion Regarding Public Transit

A survey of 200 city residents was conducted to assess support for an increase in public transit fun

Systematic Sampling Implementation

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

Traffic Flow Analysis

A transportation department uses systematic sampling to count the number of vehicles passing a check

Voter Behavior: Support for Policy X Among Different Age Groups

A political survey measured support for Policy X among two age groups. In a sample of 150 young vote

Water Quality and Fish Populations: Regression Analysis

An ecologist is studying the effect of water quality on fish populations in lakes. The regression an

Weather Patterns and Traffic Accidents

City officials are investigating the relationship between adverse weather conditions and the frequen

Basic Probability Rules in Testing Strategies

A standardized test uses different strategies when a student is uncertain about an answer. The table

BMI and Systolic Blood Pressure Regression Analysis

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

Bootstrap Sampling Distribution of the Sample Mean

A small dataset is provided, and a bootstrap resampling technique is applied to generate the samplin

Campus Computer Virus Spread: Multistage Probability Calculation

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

Casino Chips: Sum and Variance Calculation

At a casino, couples receive free chips by drawing a card from two bags. One bag (X) contains the va

Casino Free Chips Expected Sum

A casino offers free chips to couples. One person draws a card from Bag X containing the numbers $$\

Charity Lottery Expected Value Calculation

A charity holds a lottery selling 10,000 tickets at $$1$$ each. One ticket wins a prize of $$7500$$.

Comparing Bank Loan Approval Rates

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

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 Sales between Two Store Locations

Two retail stores report their average daily sales. Store 1 has a sample size of 40, with a mean dai

Comparing Manufacturing Processes for Defect Reduction

An industrial engineer is comparing two manufacturing processes to determine which one produces fewe

Effect of Fertilizer Type on Plant Growth

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

Employee Turnover Comparison in Two Departments

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

Exercise Time and Cholesterol Level Regression Analysis

A health study examining the effect of weekly exercise on cholesterol levels among 80 adults produce

Impact of Advertising on Consumer Behavior

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

Impact of Study Aid on Exam Pass Rates

A school collected data on standardized exam pass rates. Among students who used a study aid, 85 out

Insurance Sales Analysis

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

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

Restaurant Tip Percentage Analysis

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

Restaurant Wait Time Assessment

A restaurant claims that the average wait time for a table is 15 minutes. However, a study of 25 tab

Sampling Distribution of the Sample Mean from a Normal Population

A simulation experiment draws repeated random samples from a normally distributed population with $$

Scatterplot Regression Analysis on Advertising and Sales

A company collects data on its advertising budget (in thousands of dollars, x) and the resulting sal

Sleep Duration and Reaction Time Regression Analysis

A study looks at how sleep duration (in hours) affects reaction time (in milliseconds) on a computer

Smartphone Usage and Sleep Quality Regression Analysis

A study investigates whether the number of hours spent on a smartphone before bedtime affects sleep

Study Time and GPA Regression Analysis

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

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

Tip Amounts from Different Meal Services

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

Transportation Delay Times

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

Urban Traffic Volume and Air Quality

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

Voter Turnout in Two Cities

A researcher collected data on the number of people who voted in two cities during an election. In C

Website Navigation and Conversion Rates

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

Analyzing Maximum Temperatures in City A

A meteorological study collected the maximum daily temperatures over a 40-day period in City A. The

Assessing Estimators for Baseball Weight

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

Assessing Estimators in Quality Testing

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

Biased Estimator in Manufacturing

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

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 Variability in Two Measurement Methods

Two independent methods are used to measure the voltage of a battery. Method 1 produces individual m

Constructing a 95% Confidence Interval for Battery Lifetime

A quality control study tests the lifetimes of batteries. A random sample of 50 batteries has a samp

Differences in Genetic Mutations by Age

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

Employee Productivity by Shift

A company is examining the relationship between work shift (Morning vs. Evening) and productivity le

Estimator Evaluation in Quality Control

A manufacturing process is designed to produce products weighing 500 grams. Four estimators (E1, E2,

Genetic Mutations in New Fathers

It is estimated that 40-year-old men contribute on average $$65$$ genetic mutations to their offspri

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 Lifespan Probabilities

A certain brand of lightbulbs has a lifespan that is normally distributed with mean $$\mu = 1500$$ h

Movie Theater Attendance by Genre Preference

A movie theater analyzed attendance frequency based on movie genre preference. The table below categ

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

Normal Approximation to the Binomial in Sampling Distributions

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

Online Shopping Behavior: Proportion Analysis

A researcher studying online shopping behavior estimates that 30% of shoppers return items. In a ran

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 $$\

School District: Parental Involvement and Student Performance

A school district is investigating whether parental involvement is related to student performance. T

Simulation Study of Income Medians

A researcher studies household incomes, which are heavily right-skewed. The population has a median

Social Media Engagement Proportions

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

Student Extra-Curricular Participation

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

Using TI-84 for Z-Score Calculations in Sampling Distributions

A study on academic performance finds that student test scores are normally distributed with a mean

Analysis of Emergency Room Wait Times Satisfaction

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

Analysis of Survey Data on Online Learning

A survey of 150 students indicates that 90 prefer online learning. A table summarizing the responses

Analyzing Proportions as a Function of Batch Size

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

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

Comparing Defect Rates in Two Factories

Two factories, Factory A and Factory B, manufacture the same electronic component. A quality control

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

A study compared the effectiveness of two teaching methods. In a sample of 150 students taught by Me

Diet Choices by Gender

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

Digital Platform Success Rate Comparison

Two schools use different digital learning platforms. In School X, 90 out of 150 students successful

Drug Efficacy in Clinical Trials

A clinical trial is evaluating the efficacy of a new drug. In a study of 400 patients, 340 showed im

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 New Marketing Strategy

A company implemented a new marketing strategy aimed at increasing customer conversion rates during

Effectiveness of a New Vaccine

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

Estimating Customer Satisfaction

A local coffee shop surveyed 200 customers to assess their satisfaction. Out of the 200 customers, 1

Ethnicity and University Major

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

Evaluating Public Support for a Tax

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

Evaluating Strike Support

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

Evaluating Trends in Graduation Rates

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

Health Intervention Program Effectiveness

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

Hospital Safety Initiative Comparison

Two hospitals implement a safety initiative and then survey their nursing staff. In Hospital 1, 95 o

Impact of Training Program on Certification Rates

A company implemented a training program to improve certification rates among its employees. In a ra

Margin of Error Analysis in a Health Survey on Vaccination Acceptance

A health department surveys 800 random individuals about their willingness to receive a new vaccine;

Online Shopping Behavior

A survey of customers on an e-commerce website evaluated purchasing behavior across two age groups:

Political Campaign Support Analysis

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

Power Analysis in Proportion Testing

A study is being designed to detect a 5% increase in the proportion of users who prefer a new app in

Public Library Usage Survey

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

Research on Smoking Cessation Program

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

Salon Customer Satisfaction: Confidence Interval Analysis

A salon surveyed 120 customers, and 96 reported being satisfied with the service. Answer the followi

Sports Participation by Gender and Sport Type

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

Survey on Remote Work Satisfaction

A technology firm conducted a survey on remote work satisfaction among its employees. Out of 400 res

Voter Initiatives on Environmental Policy

In a survey about a new environmental policy, 600 voters were asked whether they support the initiat

Accident Rates Comparison Between Departments

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

Analyzing Machine Production Tolerances

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

Comparing Average Wait Times at Two Coffee Chains

A study is conducted to compare customer wait times at two coffee shop franchises. The following sum

Comparing Manufacturing Processes

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

Comparing New Drug Efficacy

A pharmaceutical study compares two medications for lowering blood pressure. Group 1 (Drug A) consis

Comparing Recovery Times in Two Hospitals

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

Customer Satisfaction at Two Store Branches

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

Customer Wait Time in Service

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

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

Effectiveness of a New Study Method on Test Scores

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

Employee Productivity Analysis

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

Employee Training Effectiveness

A company conducts a study to evaluate the effectiveness of a new training program. The program's im

Experience and Salary Analysis

The scatterplot below represents data on employees' years of experience (x-axis) and their annual sa

Fertilizer Impact on Plant Growth

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

Hospital Stay Duration Comparison

A hospital administration is examining the average length of patient stays in two independent units:

Light Bulb Lifespan Hypothesis Test

A company advertises that its light bulbs have an average lifespan of 1200 hours. A quality control

Nutritional Study on Caloric Intake

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

Plant Growth under Different Fertilizers

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

Simulation of Sampling Distribution for Mean Rainfall Amounts

A meteorologist simulates the sampling distribution of the average daily rainfall (in inches) record

Soil pH Variation

An agricultural experiment is conducted to assess whether a new fertilizer treatment helps bring soi

Study Hours and Exam Scores Regression

A teacher collects data from 40 students relating the number of study hours (x) to exam scores (y).

Study on Exam Anxiety Reduction

A psychologist investigates the effect of a relaxation technique on test anxiety. Twenty-five studen

Test Scores in a New Curriculum

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

Wind Speed Measurements: Station Upgrade Impact

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

Assessing the Fit of a Theoretical Distribution for Disease Rates

A health researcher claims that the incidence of a particular disease in a population is distributed

Candy Color Distribution: Chi-Square Goodness-of-Fit Test

A candy manufacturer claims that the distribution of colors in a bag of candies is as follows: red 2

Car Color and Accident Involvement: Independence Test

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

Clothing Preference and Gender: Test for Independence

A clothing store surveyed customers to see if there is an association between gender (male, female)

College Major vs Gender: Chi-Square Test for Independence

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

Customer Response to Advertising: Chi-Square Test for Independence

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

Distribution of Housing Types in a City

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

Drinking Habits and Health Outcomes: Test for Independence

A health study surveys 300 individuals, recording their drinking habits (Never, Occasionally, Regula

Drug Efficacy Across Regions: Homogeneity Test

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

Election Polls: Goodness-of-Fit for Candidate Support Ratios

In a local election survey of 500 voters, the observed support percentages for candidates were: Cand

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

Favorite Ice Cream Flavor Goodness-of-Fit Test

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

FRQ 5: Health Supplement Side Effects

A double-blind clinical trial is conducted to compare a new health supplement with a placebo. Partic

FRQ 13: Customer Loyalty Across Store Branches

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

FRQ 19: Comparing Library Usage Patterns Among Departments

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

Genetic Trait Distribution Goodness-of-Fit

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

Investigative Analysis: Public Health Awareness Survey

A public health department conducts a multi-stage survey to assess health awareness among residents

Medal Distribution across Training Groups Homogeneity Test

In a national sports event, athletes from three training groups (Group A, Group B, Group C) competed

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)

Pet Ownership and Residence Type Independence Test

A city survey collected data on pet ownership (Owning a pet, Not owning a pet) and type of residence

Public Transportation and Demographics: Chi-Square Test for Independence

City planners conducted a survey of 300 residents to determine if the preferred mode of transportati

Restaurant Popularity Goodness-of-Fit

A local food festival features four types of cuisines: Italian, Chinese, Indian, and Mexican. Organi

Species Distribution in a Wildlife Reserve

In a wildlife reserve, the theoretical model predicts that the species distribution should be: Mamma

Sports Participation and Gender – Chi-Square Test for Independence

A school conducted a survey to examine the relationship between gender (Male, Female) and participat

Survey on Preferred Modes of Transportation

A city survey investigates residents’ preferred modes of transportation. The city’s transportation m

Test for Independence: Music Preference and Age Group

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

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

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

Travel Mode and Environmental Concern – Chi-Square Test for Independence

A survey of 250 commuters collected data on their primary travel mode (Car, Public Transit, Bike) an

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

Advertising Expenditure and Product Sales

An economist investigates whether advertising expenditure (in millions of dollars) predicts product

Agricultural Yield Analysis

Agricultural scientists examine the effect of fertilizer application (in kg/ha) on crop yield (in to

Assessing Environmental Pollution Impact

A study was conducted to assess the impact of vehicle count on NO2 levels in a city. A regression an

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

Coffee Consumption and Alertness

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

Coffee Consumption and Anxiety Levels

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

Commuting Distance and Weekly Fuel Consumption

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

Dosage of Medication and Blood Pressure Reduction

A clinical researcher investigates whether the dosage of a new medication (in mg) is associated with

Dosage-Response in Drug Trials Simulation

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

Educational Study: Supplemental Tutoring Effect

A school district wants to assess the impact of additional tutoring (x, in hours per week) on math t

Effect of Experience on Salary

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

Electricity Bill vs Temperature

A utility company studied the relationship between the average monthly temperature (in $$^\circ F$$)

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 and Cholesterol Reduction

A health study investigated the effect of weekly exercise hours (x) on cholesterol reduction (y, in

Hours of Sleep and Reaction Time

A study examines the effect of hours of sleep ($$x$$) on reaction time ($$y$$, in milliseconds) for

House Price Prediction Simulation

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

Medical Dosage and Blood Pressure Response

A clinical trial tests the impact of a new medication dosage ($$x$$, in mg) on blood pressure reduct

Plant Growth and Fertilizer Amount

In an agricultural experiment, a researcher measured plant height (y, in cm) as a function of fertil

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

Robotics and Efficiency

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

Sports Performance: Practice Time vs Shooting Accuracy

A basketball coach investigates how weekly practice hours affect shooting accuracy percentages among

Sports Training and Sprint Time

A coach investigates the relationship between the number of training hours (x) and sprint time (y, i

Student Performance and Study Hours

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

Study Hours and SAT Scores: Private vs Public

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

Temperature Effects on Motor Speed

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

Temperature Impact on Soft Drink Sales

A beverage company studies the relationship between daily high temperatures (x) and soft drink sales

Tree Growth Analysis: Simulated Slope Distribution

An ecologist is studying the relationship between the age of trees and their heights. The ecologist

Water Usage and Crop Yield

An agricultural scientist is studying the relationship between water usage (in cubic meters per acre