AP Statistics FRQ Room

Advertisement Design Impact on Customer Recall

A marketing company wants to test whether two different advertisement designs lead to differences in

Basketball Free Throw Percentage Confidence Interval

A basketball player takes 80 free throws and makes 60 of them. Answer the following parts:

Car Price and Mileage Regression Analysis

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

Central Limit Theorem Verification via Simulation

A researcher has a negatively skewed population and uses simulation to draw 1000 samples of size $$n

College Graduation Rate Analysis

A college claims its graduation rate is 85%. In a survey of 200 students, 162 of them graduated with

College vs. High School Sleep Study

Two surveys measured the number of hours of sleep per night. The high school survey recorded the fol

Comparing Pass Rates for Two Classes

In a high school, two math classes took the same standardized test. In Class 1, 28 out of 35 student

Cumulative Frequency Analysis of Age Distribution

A study compares the age distributions of two different years using cumulative frequency plots. In Y

Customer Coffee Satisfaction Interval

A coffee shop surveys 50 customers to rate their satisfaction on a scale from 1 to 10. The sample ha

Customer Service Call Duration

Customer service call durations are approximately normally distributed with a mean of $$8$$ minutes

Customer Service Satisfaction by Service Type

A company surveyed 550 customers on their satisfaction level (Satisfied, Not Satisfied) with three t

Daily Step Count Hypothesis Test

A fitness app collects data from a random sample of 40 users. The sample shows an average daily step

Data Entry Error and its Impact on Summary Statistics

A delivery company recorded the number of deliveries in a day. The correct data set is: {50, 55, 60,

Examining Data Variability in Sports Statistics

A boxplot summarizes the points per game for a basketball player over a season with the following va

Impact of Study Methods on Exam Performance

A school district plans a study to determine whether group study or individual study leads to higher

Job Satisfaction Across Departments

A company administered job satisfaction surveys in two different departments. In Department 1, 120 o

Leadership Training and Employee Satisfaction

A business management study is investigating whether participation in a leadership training workshop

Lottery Ticket Analysis

The probability of winning on a single lottery ticket is $$0.001$$. A person buys tickets one after

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

Nutrition Study: Effects of Diet on Weight Loss

A nutritionist intends to study whether different diets lead to different average weight losses over

Public Opinion on School Length: Categorical Data Summary

In a survey of 2000 parents regarding their preference for the length of the school year, the respon

Remote Learning Preference in High Schools

Two high schools surveyed their students regarding their preference for remote learning. In School A

Sampling Distribution of Average Purchase Amount

Individual consumer purchase amounts are normally distributed with a mean of $$50$$ dollars and a st

Sampling Distribution of the Sample Range for SAT Scores

A statistician is studying SAT scores whose distribution is known to have a certain degree of variab

Simulation of Sampling Distribution of a Proportion in a Medical Recovery Study

In a clinical trial, suppose the true proportion of patients who recover from a treatment is 0.80. A

University Course Selection by Gender

A university survey of 300 students recorded their course selection (STEM or Humanities) and gender

Water Filtration Systems and Water Quality

A city planning department is studying the impact of different water filtration systems on the quali

Z-Scores and Percentile Ranks in a Test Examination

Assume that the scores on a standardized test are normally distributed with a mean of $$80$$ and a s

Art Exposure and Creativity Scores

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

Assessing the Sampling Distribution of Predicted Values in Linear Regression via Simulation

In a study examining the relationship between advertising expenditure (x) and sales (y), a simulatio

Call Duration Analysis in a Service Center

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

Chi-Square Analysis for Dietary Habits and Exercise Frequency

A nutrition study classifies 300 individuals by their dietary habit (Vegetarian, Non-Vegetarian) and

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

Difference in Response Rates for Two Advertisements

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

Environmental Study: Air Pollution vs. Respiratory Issues

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

Food Safety Inspections in Restaurants

In a restaurant chain, historical data show that 10% of health inspections result in a violation. In

Impact of Study Environment on Academic Achievement

A survey of 100 students collected data on their study environment (categorized as 'Quiet' or 'Noisy

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

Museum Visits and Visitor Satisfaction

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

Quality Control in a Bakery

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

Residual Plot Analysis for a Blood Pressure Study

A medical study uses a regression model to predict blood pressure (Y) from sodium intake (X). The re

Retail Promotions: Sales vs Advertising Budget

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

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 Engagement Study

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

Student Preference Survey

A school conducted a survey to determine students' favorite extracurricular clubs, recording two cat

Wait Time and Meal Satisfaction

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

Website A/B Testing for Click-Through Rates

A technology company is testing two versions of its website (Version A and Version B) to see which o

Analyzing Sampling Variability with Box Plots

A study is conducted to estimate the average test score for teachers in a school district. Four diff

Bias in Random Digit Sampling

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

Calculating and Interpreting a Confidence Interval from Water Quality Data

A study measures the concentration of a contaminant in a river. A random sample of 25 measurements y

Cluster Sampling in Educational Research

A researcher wants to study academic performance across a large school district. The district is div

Comparing Sampling Variability Across Methods

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

Comparing Two Treatments in a Medical Study

A clinical trial compares two treatments for lowering blood pressure. Treatment A (n = 25) results i

Customer Loyalty Programs: New vs. Established Store

A retail chain is evaluating the effectiveness of their customer loyalty programs. In a survey, 70 o

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

Differences in Data Collection Techniques: Face-to-Face vs. Online Surveys

A political research firm collects survey data about voter opinions through both face-to-face interv

Effect of Diet on Cholesterol Levels

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

Effectiveness of a Training Program on Certification Outcomes

In a study evaluating a certification training program, 80 employees who attended the training had 6

Effectiveness of Stress Reduction Methods: Yoga vs. Meditation

A wellness center studied the effectiveness of yoga and meditation on reducing stress. In the yoga g

Energy Conservation Campaign and Household Energy Use

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

Evaluating Bias in Voluntary Response Surveys

A local government agency conducts a survey on community satisfaction with public transportation thr

Evaluation of Experimental Design and Inference in Consumer Behavior Studies

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

Heart Rate Recovery and Fitness Level

In a cardiovascular fitness study, researchers examine if higher fitness levels (measured by a fitne

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

Impact of Diet on Weight Loss Success

A nutritionist compared the success rates of two different diet plans. Under Diet A, 45 out of 75 pa

Impact of Sample Size on Confidence Interval Width

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

Impact of Undercoverage Bias on Survey Results

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

Physical Activity and Cognitive Function in Older Adults

Researchers are investigating whether increased physical activity is associated with better cognitiv

Retail Customer Purchase Binomial Model

A retailer estimates that the probability of a customer making a purchase during a visit is 10%. On

Retail Store Checkout Efficiency Study

A study compared the average waiting time at checkout between two methods in a retail store. For the

Sampling Variability in Teacher Performance Evaluations

A school district collects teacher performance evaluations through student surveys. The administrati

Temperature and Ice Cream Sales: A Summer Analysis

During the summer, a study was undertaken to analyze whether higher daily temperatures increase ice

Traffic Flow System and Commuting Times

A city is testing a new traffic flow system designed to reduce commuting times during rush hour. The

Voting Patterns in a Retrospective Study

A retrospective study collected exit poll data to determine the level of support for Policy X among

Ad Spend and Market Share Regression Analysis

A market analyst investigates the relationship between advertising spend (in millions of dollars) an

Apartment Rental Prices Estimation

A real estate researcher is studying monthly apartment rents in a metropolitan area. In a random sam

Binomial Process in Quality Testing

A quality control inspector tests a batch of 100 light bulbs. Each bulb has a 10% chance of being de

Car Purchase Decisions by Region

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

Carnival Game Payoff Transformation

In a carnival game, the possible winnings are $$2$$ dollars with probability $$0.5$$, $$5$$ dollars

Charity Lottery Expected Outcome

A charity sells 10,000 lottery tickets at $1 each with one prize of $7500. Let $$X$$ represent the n

Defect Rate Comparison between Two Factories

A manufacturing company is studying defect rates in two of its factories. Factory 1 produced 1000 it

Dice Roll Sum Analysis

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

First Honest Encounter: Geometric Distribution

In ancient Greece, suppose only 12% of men are honest. Let \(X\) represent the trial on which the fi

Fitness Center Membership Duration

A fitness center wishes to estimate how long its members typically stay subscribed. A random sample

Game Show Strategy with Random Variables

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

Geometric Distribution in Reliability Testing

A machine in a factory has a 5% chance of failing on any given day. Let $$X$$ denote the day on whic

High School SAT Scores Analysis

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

Impact of Social Media Usage on Academic Performance

A study is conducted to examine the relationship between time spent on social media and academic per

Medical Trial for a New Drug

A pharmaceutical company is conducting a clinical trial to test the efficacy of a new drug in reduci

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

Pharmaceutical Study: Recovery Time Distribution

A pharmaceutical study records recovery times (in days) for a treatment with the following distribut

Public Opinion Survey on Local Issues

A political analyst is conducting a survey to gauge public opinion on various local government polic

Quality Control Binomial Process

A manufacturing process produces items such that each item has a $$5\%$$ chance of being defective.

Restaurant Tips: Analysis of Random Variables

In a restaurant, tips received follow this distribution: $$0$$ dollars (p = 0.1), $$5$$ dollars (p =

Retail Customer Purchases: Random Variable Analysis

A survey at a retail store reveals that the number of items purchased per visit follows this distrib

Student Exam Score Distribution

An exam produces scores in the following intervals with corresponding percentages. Use the midpoints

Student Study Hours and Exam Performance Regression Analysis

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

Student Test Scores and Conditional Probabilities

A school's data on test strategies and score ranges is summarized in the tables below. Table 1: Str

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 =

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

Yearly Savings and Investment Return Regression Analysis

A financial analyst studies the effect of yearly savings (in thousands of dollars) on the rate of in

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 Variability in a Manufacturing Process

A factory produces 1-liter plastic bottles with the volume of each bottle normally distributed aroun

Caffeine Content Analysis

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

Caffeine Content Analysis in Energy Drink Boxes

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

Caffeine Content in Energy Drink Boxes

An energy drink manufacturer advertises that each bottle contains on average 200 mg of caffeine with

Comparing Pass Rates Between Two Schools

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

Comparing Sampling Distribution of the Sample Mean in Normal vs. Skewed Populations

Two populations, A and B, both have the same mean $$\mu = 100$$ and standard deviation $$\sigma = 20

Comparing School Test Scores

School A has a test score distribution with a mean of 75 and a standard deviation of 8, and School B

Comparing Teaching Methods

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

Differences in Genetic Mutations by Age

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

Election Polling Proportions

In a pre-election survey, it is known that 52% of voters favor a certain candidate. A random sample

Emergency Room Wait Times Analysis

In a hospital, emergency room wait times are approximately normally distributed with a mean of 30 mi

Employee Productivity by Shift

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

Environmental Concerns by Community Type

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

Evaluating Genetic Mutations in New Fathers

A study examines the number of genetic mutations passed on by new fathers of different ages. It is e

Examining Bias in Sample Maximums

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

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

Sampling Distribution for Differences in Sample Means: Academic Test Scores

Two classes are compared on a standardized test. Class A has a population mean of 78 with a standard

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 $$\

Sampling Distribution of Differences in Proportions

In a study of customer eating habits at two fast‐food restaurants, it was observed that at Restauran

Sports Performance Data Analysis - Batting Averages

In a baseball league, the average batting average is 0.280 with a standard deviation of 0.030. A coa

Student Extra-Curricular Participation

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

Training Techniques and Marathon Finish Times

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

Using TI-84 Functions for Normal Probability

Assume that a dataset follows a normal distribution with mean $$\mu = 75$$ and standard deviation $$

Website Load Time Evaluation

A popular website has load times that are approximately normally distributed with a mean of 3.5 seco

Website Visit Duration Analysis

On a particular website, user visit durations are normally distributed with a mean of 4 minutes and

Assessing Customer Satisfaction in a Retail Store

A retail store surveys 200 customers and finds that 150 are satisfied with their shopping experience

Assessing the Fairness of a Die

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

Coffee Shop Loyalty

A coffee shop chain is investigating customer loyalty. A survey at the downtown branch (Group A) sam

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 Test Pass Rates

A study compares the pass rates of two types of schools. The following table summarizes the results:

Comparing Two Dietary Supplements

A study compares two dietary supplements. In a sample of 200 consumers for Supplement A, 140 reporte

Comparing Two Proportions: Online vs. In-Store Shopping Preferences

A researcher compares shopping preferences. In a sample of 300 online shoppers, 210 prefer online sh

Comprehensive Analysis of Confidence and Significance in Survey Data

A political researcher conducted a two-part survey to analyze voter opinions on a new policy. The fi

Confidence Interval for Social Media Users

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

Customer Preference Difference Between Cities

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

Customer Satisfaction Survey by Region

A retail company conducted a customer satisfaction survey in two regions, North and South. Responses

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

Effectiveness of a New Vaccine

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

Employee Retention in a Tech Firm

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

Estimating Customer Satisfaction

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

Impact of a New Regulation

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

Impact of Training Program on Certification Rates

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

Influence of Advertisement Exposure on Product Purchase

A marketing study examined whether exposure to an advertisement influences the likelihood of purchas

Job Satisfaction by Shift Work

A hospital survey examined job satisfaction among nurses working on the Day Shift and the Night Shif

Political Polling: Candidate Approval

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

Political Polling: Estimating Voter Support

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

Public Health: Influenza Vaccination Rates

A public health study compares influenza vaccination rates between urban and rural areas. In urban a

Public Opinion on Policy Change

A survey is conducted on a new tax policy. In a simple random sample of 500 voters, 260 indicated th

Public Survey on Recycling: Urban vs. Rural

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

School Lunch Program Participation

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

Significance Testing of Proportion Differences in Crime Rates

In a survey, 55 out of 200 residents in City A and 40 out of 250 residents in City B reported feelin

Social Media Usage by Gender

A survey compares social media usage among different genders. In a sample of 400 males, 320 use soci

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

Survey on Remote Work Satisfaction

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

Traffic Accident Analysis

A study on traffic accidents examined the severity of accidents (Severe vs. Minor) and the driver’s

Vaccine Acceptance Rates

Researchers want to compare vaccine acceptance between urban and rural populations. In an urban area

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

Web Advertisement Click-Through Rates

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

Assessing Training Effects on Marathon Times

A sports scientist is evaluating the effect of a new training regimen on marathon finishing times. T

Comparative Analysis of Daily Sales at Two Branches

Two branches of a store report their average daily sales. Branch A has a sample of $$n=30$$ with a m

Comparative Analysis of Lecture Techniques Using Paired Data

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

Comparing Average Wait Times at Two Coffee Chains

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

Customer Satisfaction Survey

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

Daily Energy Consumption Analysis: Hypothesis Test

A consumer agency is investigating a claim that a new brand of air-conditioning units uses only $$6.

Effectiveness of Drug Treatments

A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients

Employee Productivity Analysis

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

Energy Consumption Analysis

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

Enzyme Activity Confidence Interval

A laboratory measures enzyme activity in 12 samples. The sample mean enzyme activity is 7.5 units wi

Evaluating a Mobile App's Impact on Daily Step Count

A health technology firm develops a new mobile application aimed at increasing daily physical activi

Investigative Analysis of Customer Service Performance Metrics

A company collects data on customer service performance across two centers. For a focused study on c

Machine Downtime Analysis

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

Online Platform User Engagement

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

Paired t-Test for Sleep Duration with Meditation Program

A study is conducted to evaluate the effect of a four-week meditation program on sleep duration. For

Physical Activity and Cholesterol Levels

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

Production Efficiency Comparison Across Shifts

A factory compares production times between two work shifts. Shift A has a sample mean production ti

Quality Control in Food Packaging

A snack food company advertises that its bags contain 305 grams of product. To ensure quality, a ran

Quality Control: Machine Calibration

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

Sample Size Effect on Component Length Confidence Interval

In a manufacturing process, the length of a component is measured. A sample of measurements yields a

Simulation of Sampling Distribution in a Clinical Trial

A medical researcher conducts a simulation to analyze the sampling distribution of the mean systolic

Simulation of the Sampling Distribution for Mean Salary

A company's HR department conducts a simulation study to understand the sampling distribution of the

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 Sleep Duration Effects

A research study investigates whether sleep duration affects employee productivity. In a random samp

Temperature and Electricity Consumption Analysis

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

Testing Mean Daily Coffee Consumption Claim

A claim is made that college students drink an average of at least 2.5 cups of coffee per day. A sur

Workplace Wellness Program Evaluation

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

Candy Color Distribution Goodness-of-Fit Test

A candy manufacturer claims that the distribution of candy colors in a bag is 30% red, 20% blue, 25%

Clinical Trial: Treatment Effects on Recovery Rates

In a clinical trial, patients are randomly assigned to one of three treatment strategies (Treatment

Customer Satisfaction Survey Across Store Locations

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

Diet Preference Among Athletes

In a study, three groups of athletes (Football, Basketball, Soccer) were surveyed regarding their di

Drug Side Effects Analysis: Chi-Square Test for Independence

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

Employee Training Program: Comparing Certifications Across Departments

A company is evaluating the effectiveness of a new training program by comparing certification rates

Examining Health Outcomes by Smoking Status

Researchers are interested in determining if there is an association between smoking status and heal

Favorite Ice Cream Flavor Goodness-of-Fit Test

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

FRQ 2: Association Between Smoking Behavior and Gender

A public health survey collected data on smoking status and gender from 150 individuals. The observe

FRQ 6: Association Between Diet and Heart Disease Risk

A study investigates whether there is an association between diet type and heart disease risk. The s

FRQ 13: Customer Loyalty Across Store Branches

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

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

Goodness-of-Fit Test for Dice Fairness

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

Homogeneity in Dietary Habits Across Regions

Nutrition researchers surveyed individuals from three regions regarding their dietary habits: Omnivo

Homogeneity in Student Class Preferences

Three high schools conducted surveys to determine whether student preferences for online versus in-p

Independence Test: Technology Adoption and Age Group

A survey of 600 consumers categorized by age group (Young, Middle-aged, Senior) recorded whether the

Independence Test: Voting Preference and Gender

A survey of 500 voters collected data on voting preference (Candidate A, Candidate B, Other) and gen

Job Satisfaction Among Different Occupations

A study is conducted to compare job satisfaction among four occupational groups in a school system:

Observations of Wildlife Distribution

A wildlife biologist expects that four bird species in a habitat occur in equal proportions. In a su

Pet Ownership in College Residences

A study investigates whether there is an association between college residence type and pet ownershi

Preferred Payment Methods: Chi-Square Test for Homogeneity

A market research firm conducted surveys in three different cities regarding preferred payment metho

Quality Control in a Factory

A factory has three production lines, each producing 100 items. Quality control involves checking fo

Survey on Preferred Modes of Transportation

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

Traffic Accident Severity

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

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

Vehicle Type Distribution Goodness-of-Fit Test

At a busy toll plaza, vehicles are classified into three types: Cars, Trucks, and Motorcycles. Based

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

Weather Patterns and Energy Consumption

A utility company is interested in whether weather conditions are associated with high or low energy

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

Assessing Environmental Pollution Impact

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

Blood Pressure and Sodium Intake Study

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

Climate Change: CO2 Concentration vs Global Temperature Simulation

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

Coffee Consumption and Alertness Score

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

Dosage of Medication and Blood Pressure Reduction

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

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 $$^\circ F$$)

Engine Size and Emissions

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

Examining Crop Yield from Rainfall

Researchers are investigating the relationship between the amount of rainfall (in inches) during the

Fish Population and Pollution Levels

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

Height and Weight Relationship: Male vs Female

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

House Price Prediction Simulation

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

Impact of Fertilizer Type on Plant Growth

A researcher is studying the effect of two different fertilizers on plant growth. The amount of fert

Machine Runtime and Maintenance Costs

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

Manufacturing Quality Control

A quality control engineer investigates the relationship between machine operation time (in hours) a

Manufacturing Quality Control: Regression Parameter Optimization Simulation

A quality control engineer is analyzing the relationship between machine operating speed (in m/s) an

Online Engagement and Sales Conversion

An e-commerce analyst studied the relationship between average time spent on a website (in minutes)

Practice Time and Music Performance Skill

A study investigates the effect of weekly practice hours ($$x$$) on a music performance skill score

Real Estate Regression Analysis

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

Relationship Between Hours Studied and Test Scores

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

Social Media Use and Academic Performance

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

Software Development Efficiency: Lines of Code and Bug Count

A software company wants to study whether the number of lines of code written in a project is relate

Sports Training and Sprint Time

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

Temperature and Electricity Consumption

A power company studies the relationship between daily average temperature (in °C) and electricity c

Temperature Effect on Ice Cream Sales

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