AP Statistics FRQ Room

Analysis of Weather Data: Daily Rainfall

A meteorologist recorded daily rainfall (in mm) over a month and summarized the data in the followin

App Usage: Comparing Two Advertising Campaigns

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

Bootstrap Simulation of the Sampling Distribution of the Median Salary

Given the salary data $$\$3000$$, $$\$7000$$, $$\$15000$$, $$\$22000$$, $$\$23000$$, and $$\$38000$$

Calculating Variance and Standard Deviation for Book Counts

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

Categorical Data Analysis: Survey on Preferred School Year Length

A survey of 2000 parents asked about their preference for the length of the school year. The respons

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 Cumulative Frequency Graphs for Age Distributions

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

Cumulative Frequency Curves: Comparing 1860 and 1980 U.S. Populations

Cumulative frequency curves for the U.S. population in 1860 and 1980 are provided. For 1860, half th

Customer Satisfaction in Two Regions

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

Effect of Outliers on the Sampling Distribution of the Mean

Consider two populations of student test scores. Population A does not contain extreme scores while

Holiday Shopping Behavior: In-Store vs Online

During the holiday season, a survey was conducted on shopping behavior. Among 300 in-store shoppers,

Home Run Distance Analysis

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

Internet Usage Among College Students

A survey of 220 college students recorded the number of hours they spend online per day. The results

Interquartile Range and Boxplot Construction

Given the dataset: {12, 15, 16, 18, 20, 22, 25, 27, 30, 35}, perform an analysis of its distribution

Investigative Analysis of Public Health Survey on COVID-19

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

Irrigation Techniques and Crop Yield

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

Lottery Ticket Analysis

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

Measures of Variability in Teacher Ages

The ages of 12 mathematics teachers at a high school are: {24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 5

Mobile Device Battery Life

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

NBA Wins: Analyzing Back-to-Back Stem Plots

A back-to-back stem plot displays the number of wins for NBA teams from the Eastern and Western Conf

New Product Defects

A new product is manufactured with a defect rate of $$0.01$$. In each production batch containing 50

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

Online vs. In-Person Instruction on Language Course Retention

An educational study is designed to compare the effectiveness of online versus in-person instruction

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

Restaurant Wait Time Analysis

A consumer group claims that a certain fast-food restaurant’s average wait time is 4 minutes. They c

Sampling Distribution and Confidence Interval Implications for Household Incomes

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

Sampling Distribution of the Median in a Skewed Production Process

A factory produces components whose lifespans (in hours) are right-skewed due to occasional defects.

Simulation of the Sampling Distribution for the Sample Variance

Consider a normally distributed variable with a true variance of $$\sigma^2 = 16$$. A researcher sim

Sports Performance: Basketball Free Throws

A basketball player makes free throws with a success probability of 75%. In a game, she attempts 20

Subway Train Arrival Times

Subway wait times are normally distributed with a mean of $$5$$ minutes and a standard deviation of

Survey of Smartphone Usage Time

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

Treatment Outcomes in Hospital Study

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

Analyzing Temperature vs. Ice Cream Sales

An ice cream shop collected data over a summer month to assess the relationship between daily temper

Assessing a New Drug's Efficacy

A clinical trial was conducted to determine the effect of a new drug's dosage (x, in mg) on patient

Athletic Performance Correlation Analysis

A study on athletes observed the relationship between hours of training per week (x) and competition

College Major by Gender

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

Comparing Regression Lines for Calorie Consumption in Two Groups

A study compares the relationship between body weight (x) and calorie burn (y) for two groups: men a

Computing Regression Statistics from Summary Data: Advertising and Sales

A market research study investigates the relationship between advertising expenditure (X, in thousan

Customer Return Rates for Two Brands

A market research firm collected data on customer return behavior for two competing clothing brands.

Dietary Effects on Blood Pressure

A research study is being conducted to assess the effects of a low sodium diet on blood pressure amo

E-Commerce Site Traffic and Revenue Analysis

An e-commerce website collected data on daily visitor counts (x) and corresponding sales revenue in

Health Study on Diet and Activity

A health study investigated the relationship between diet type (Vegetarian vs. Non-vegetarian) and a

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

Predicting Student Exam Scores from Study Hours

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

Retail Promotions: Sales vs Advertising Budget

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

Sampling Distribution of the Coefficient of Determination (\(r^2\)) via Simulation

Researchers study the relationship between study time and exam scores and want to understand the sam

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 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

Smartphone Brand Loyalty

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

Social Media Activity and Face-to-Face Interactions

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

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

Study Time and Test Scores Relationship

A teacher collected data on the number of hours 25 students studied for a final exam and their corre

Temperature and Ice Cream Sales

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

Training Hours and Error Rates in Manufacturing

A manufacturing firm collected data for 50 employees on the number of training hours received (x) an

Analysis of Recycling Behavior

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

Assessing the Impact of Sampling Bias through Simulation

A researcher suspects that a nonrandom sampling method may introduce bias into estimates of a popula

Central Limit Theorem Demonstration Through Simulation with an Exponential Population

A researcher is interested in the Central Limit Theorem (CLT) and performs a simulation by drawing s

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

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

Evaluating Survey Sampling Methods

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

Evaluating the Effectiveness of a New Drug

A clinical trial compared a new drug with a placebo regarding patient recovery. The data are summari

Experimental Design: Evaluating a Review Course for SAT Scores

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

Impact of Advertising on Product Purchase

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

Impact of Undercoverage Bias in Voter Surveys

A national polling organization uses a telephone directory to sample voters for an upcoming election

Impact of Undercoverage Bias on Survey Results

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

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 Response Time in Emergency Calls

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

Music Therapy and Stress Levels

A study is designed to test whether music therapy can reduce stress levels in adults. A double-blind

Randomized Block Design in Evaluating a Teaching Method

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

Teaching Methods and Student Performance

A school wants to compare the effectiveness of two different teaching methods on student performance

Using Random Digit Tables in Clinical Studies

In designing a clinical study, researchers decide to use a random digit table to select a simple ran

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

City Traffic Speed Analysis

The city transportation department collected data on the speeds of vehicles on a major highway. A ra

Comparison of Accident Rates on Highway Sections

A study on highway safety compared accident rates on two sections of a highway. On Section A, 5 acci

Comparison of Incident Rates between Day and Night Shifts

In a manufacturing plant, incident reports were recorded over a month. The Day shift experienced 15

Customer Satisfaction Survey

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

Daily Steps and Calorie Burn Regression Analysis

A fitness study examines the relationship between the number of daily steps (in thousands) and calor

Defects from Two Machines

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

Energy Consumption Random Variables

In a small town, the daily household energy consumption (in kWh) is modeled by the following distrib

Fitness Class Participation by Age Group

A gym surveyed 300 members about their preferred fitness class types. The results by age group are d

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

Lottery Ticket Expected Outcome

A lottery ticket costs $2. The possible outcomes are: win $100 with probability 0.01, win $20 with p

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 Learning vs. Traditional Classroom Formats

An educational researcher is studying the effectiveness of online learning compared to traditional c

Parental Involvement and Child's Academic Performance Regression Analysis

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

Political Polling: Voting Intentions by Age Group

A polling agency surveyed 300 voters about their intention to vote 'Yes' or 'No' on a particular iss

Quality Control Binomial Process

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

Raffle Ticket Payouts in a Fundraiser

A charity raffle sells 500 tickets at $2 each. There is one main prize of $800 and two smaller prize

Random Variable Transformation in a Carnival Game

A carnival game offers three possible payouts: $$\$2$$ with probability 0.5, $$\$5$$ with probabilit

Sampling Distribution of the Sample Median from a Skewed Distribution

A simulation is conducted by drawing samples from a right-skewed distribution. For each sample, the

Satellite Data and Weather Forecast Accuracy Regression Analysis

A meteorologist analyzes the impact of satellite observation quality (rated on a scale from 0 to 10)

Simulated Sampling Distribution of Survey Proportions

A researcher simulates survey responses where each respondent answers 'Yes' or 'No' with a true prob

Sleep Duration and Reaction Time Regression Analysis

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

Startup Daily Profit Analysis

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

Student Exam Score Distribution

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

Student Testing Strategy and Scores Analysis

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

Traffic Accident Analysis

A city records the number of traffic accidents per day over a month. The observed distribution is gi

University Dining Hall Food Quality Survey

A survey of university dining hall patrons was conducted to assess food quality. Out of 200 responde

University Exit Exam Pass Rate

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

Urban Traffic Volume and Air Quality

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

Analyzing Daily Coffee Sales Sampling Distribution

A local coffee shop claims its daily sales (in dollars) are normally distributed with a mean of $$\m

Assessing Bias in Weight Measurements

A shipping company is evaluating three different types of scales (A, B, and C) for measuring package

Assessing Estimators in Quality Testing

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

Comparing Durability of Lightbulbs

A study was conducted to compare the longevity of light bulbs manufactured by two different factorie

Confidence Interval and Sampling Distribution in Height Estimation

A researcher aims to estimate the average height of college students with a margin of error of $$1$$

Diet Preferences and Exercise Habits

A health survey sought to determine if there is any association between an individual’s diet prefere

Difference in Proportions: Fast Food Restaurant Study

A study compares customer behavior at two fast-food restaurants. At the revamped restaurant, $$25\%$

Effect of Sample Size on Variability of Estimator

A researcher collects repeated samples from a population with a known mean of $$\mu = 100$$ and stan

Evaluating Customer Satisfaction Proportions

A restaurant chain wants to compare customer satisfaction between two of its locations. At Restauran

High Math Anxiety and Brain Activity

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

Music Streaming Service Satisfaction

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

Normal Approximation for Binomial Proportions

In a large survey, $$65\%$$ of respondents favor a new policy. In a random sample of $$100$$ respond

Political Opinion Poll on Policy Support

A political opinion poll was conducted to determine the relationship between political affiliation a

Polling Data Analysis

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

Quality Control in Baseball Production

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

Quality Control in Manufacturing: CLT Application

A manufacturing plant produces metal rods whose lengths are not normally distributed, but have a pop

Quality Control of Production Errors

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

Sampling Distribution for Sample Proportions: Political Polling

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

Sampling Distribution of Proportions: Defective Products

A factory produces electronic components with a defect rate of 3%. A quality inspector randomly samp

Simulation of Dream Recall Sampling Distribution

A study records the number of dreams high school students remember each night. The population median

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

Stock Returns Probability Calculation

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

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

Analyzing Election Poll Data: Estimating the Margin of Error

An election poll of 1000 voters produced a sample proportion of $$\hat{p}=0.48$$ for Candidate A. As

Analyzing Proportions as a Function of Batch Size

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

Business Model Customer Return Rate Comparison

A company compares two business models by examining customer return rates. For Model A, 312 out of 5

Customer Loyalty Program Impact Study

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

Customer Satisfaction: In-Store vs. Online Shoppers

A retail store conducted a survey. Among in-store shoppers, 340 out of 400 reported being satisfied,

Digital Platform Success Rate Comparison

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

Effect of an Advertisement on Purchase Intent

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

Effectiveness of a Social Media Campaign

A company launched a social media campaign to increase brand engagement. Two surveys were conducted:

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 Social Media Usage Proportions

A research study surveyed 750 social media users to estimate the proportion who use a specific app d

Evaluating Trends in Graduation Rates

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

Health Study: Smoking Prevalence Comparison

A health study compared the smoking prevalence between two cities. In City A, a sample of 500 respon

Hospital Infection Rates: Hypothesis Testing

A hospital claims that its post-surgery infection rate is 2%. In a sample of 500 patients, 18 develo

Job Satisfaction by Shift Work

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

Measuring Customer Preferences

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

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 Opinion Poll Analysis

A political poll was conducted to assess support for a proposed tax bill. In a simple random sample

Quality Control in Manufacturing

A manufacturing quality control team is checking the proportion of defective items in a production b

Retail Customer Satisfaction Survey Design

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

Sample Size Determination for Desired Margin of Error

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

Smoking Status and Respiratory Illness

Hospital records show data on patients' smoking status and whether they have a respiratory illness.

STEM Club Gender Representation Study

A high school is investigating the proportion of female members participating in its STEM clubs. Par

Student Opinion on School Lunch Quality

A survey of 250 students at a high school found that 180 students reported that the school lunches a

Test of a Hypothesis on Voter Turnout

A political analyst claims that at least 60% of registered voters participate in elections. A sample

University Policy Support Analysis

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

Urban vs Rural Voter Support Analysis

A political poll collected data from two independent groups: urban voters and rural voters. In the u

Voter Approval Poll Design

A polling organization samples voters to estimate the proportion of the electorate that approves of

Voter Preference by Region

In a political poll, 400 voters from Region 1 were surveyed, and 220 indicated support for a particu

Voting Patterns on Renewable Energy

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

Average Household Electricity Usage

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

Battery Lifespan Comparison

Two battery manufacturers are being compared based on the lifespan of their batteries. For Manufactu

Career Development Program

A corporation has implemented a career development program and wishes to assess its impact on employ

Comparing Manufacturing Processes

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

Comparing Two Diet Programs on Weight Loss

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

Comparing Two Diets

A nutritionist compares the effects of two diets on weight loss. In a study, Diet 1 (n = 30) results

Diet Program Effectiveness

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

Effect of a New Diet on Weight Loss

A nutritionist is evaluating a new diet plan by measuring the weight loss of 24 participants over a

Employee Training Effectiveness

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

Energy Consumption Analysis

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

Engine Emissions Compliance

An environmental agency is monitoring engine emissions to ensure compliance with regulations that re

Hospital Stay Duration Comparison

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

Impact of Training Programs on Test Scores

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

Investigative Analysis of Customer Service Performance Metrics

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

Manufacturer's Claim on Product Weight

A manufacturer claims that its product has an average weight of 50 grams. A study measuring 40 produ

Manufacturing Process Improvement

A manufacturing company implements a new process intended to reduce component production times. For

Public Transportation Use and Environmental Awareness

A survey examines whether public transportation usage is related to environmental concern. Participa

Rainfall Measurement Study

A meteorologist records daily rainfall (in mm) over 20 days in a region. The sample has a mean of 12

Reaction Time Testing Under Caffeine Effects

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

Simulating Sampling Distribution of Chip Weight

A chip manufacturing factory is investigating the average weight of its chips. A simulation was perf

Simulating Sampling Distribution of Daily Temperatures

A simulation study was conducted to generate the sampling distribution of the sample mean daily temp

Simulation of Sampling Distribution for Mean Crop Yield

An agricultural researcher is interested in the average crop yield (bushels per acre) of a particula

Temperature and Electricity Consumption Analysis

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

Temperature and Ice Cream Sales Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and the number of ice cream con

Voting Behavior and Political Affiliation

A study analyzes voting behavior among members of two political parties, Party A and Party B. The da

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

Workplace Wellness Program Evaluation

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

Association between Exercise Frequency and Diet Type

A survey of 200 college students examines whether there is an association between exercise frequency

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

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

College Major vs Gender: Chi-Square Test for Independence

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

Consumer Brand Preference Homogeneity Test

A consumer survey was conducted comparing brand preference for three competing brands (Brand X, Bran

Consumer Preference Survey: Chi-Square Goodness-of-Fit

A fast‐food restaurant expects that there is no preference among four new burger flavors. To test th

Customer Satisfaction Across Regions

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

Dice Fairness Goodness-of-Fit Test

A game designer claims that a six-sided die is fair, such that each face appears with probability $$

Diet and Exercise Frequency: Independence Test

A health study of 240 participants recorded data on diet quality (Healthy, Unhealthy) and exercise f

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

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

Drug Side Effects Analysis: Chi-Square Test for Independence

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

Effect of Marketing Campaign on Brand Awareness

A company wishes to determine if exposure to its marketing campaign is associated with brand awarene

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

FRQ 1: Distribution of Customer Preference for a New Snack

A snack company claims that the preferences for flavors of its new snack follow the proportions: Fla

FRQ 3: Voter Preferences by Age Group: A Homogeneity Test

A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup

FRQ 11: Distribution of Emergency Calls by Time of Day

A city’s fire department expects that emergency call volumes vary by time of day according to histor

FRQ 13: Customer Loyalty Across Store Branches

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

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

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

Homogeneity in Student Class Preferences

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

Job Satisfaction Across Departments: Chi-Square Test for Homogeneity

An organization wants to compare job satisfaction among employees in three different departments: Sa

Manufacturing Quality Control: Chi-Square Goodness-of-Fit

A bolt manufacturing process is expected to produce bolts in four size categories in the proportions

Patient Outcomes by Treatment: Chi-Square Test for Independence

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

Political Party and Environmental Concern

A survey studies the relationship between political party affiliation (Democratic, Republican, Indep

Preferred Study Methods: Homogeneity Test Across Colleges

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

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

Quality Control in a Factory

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

Smartphone Brand Preference

A market research firm expects that smartphone brand preferences will follow the proportions: Brand

Social Media Usage Among Age Groups: Independence Test

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

Socioeconomic Status and Book Reading Frequency: Independence Test

A survey of 600 individuals collects data on their socioeconomic status (Low, Medium, High) and book

Student Extracurricular Activities: Chi-Square Goodness-of-Fit

A high school believes that student interest in extracurricular activities (Sports, Music, Drama, Cl

Survey Response Distribution Goodness-of-Fit Test

A survey on public opinion regarding a new policy asks respondents to choose among Agree, Neutral, a

Test for Independence: Music Preference and Age Group

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

Traffic Light Malfunction Analysis

A city’s transportation department monitors traffic light performance. They expect that 90% of signa

Voter Turnout by Age Group: Test for Independence

A survey reports voter turnout among four age groups: 18-29, 30-44, 45-64, and 65+. The two variable

Advertising Budget and Revenue

A study on 25 companies examines the relationship between advertising budget (x, in thousands of dol

Advertising Budget and Sales Revenue

A company collected data on weekly advertising expenditure ($$x$$, in thousands of dollars) and corr

Age and Reaction Time Study

A cognitive psychology study examines the relationship between age (in years) and reaction time (in

Assessing Environmental Pollution Impact

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

Biking Speed and Heart Rate

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

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

Daily Steps vs Calorie Burn

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

Daily Water Intake and Blood Pressure

A nutrition researcher studied the relationship between daily water intake (in liters) and systolic

Effects of Weather on Tourist Visits

The city tourism board collected data to study the relationship between daily high temperature (in °

Employee Performance from Experience

An HR department collected data on 28 employees to understand how years of experience (x) affect per

Energy Consumption and Temperature: Simulation Study

A data analyst is investigating the relationship between ambient temperature (in $$^\circ C$$) and h

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

Exercise Duration and Weight Loss

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

Exercise Frequency and Resting Heart Rate

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

Fish Population and Pollution Levels

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

Hours of Sleep and Reaction Time

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

Ice Cream Sales vs Temperature

A local ice cream shop recorded daily temperature (in $$^\circ F$$) and sales revenue (in dollars) o

Manufacturing Process Optimization

A production manager investigates the relationship between machine speed (in units per minute) and p

Noise and Concentration Scores

Researchers are exploring the relationship between ambient noise (x, in decibels) in a study environ

Physical Activity and Weight Loss: Simulation Analysis

A researcher is studying the effect of weekly physical activity (in hours) on weight loss (in kg) us

Predicting Ice Cream Sales from Temperature

In a study of 25 summer days, data were collected on daily maximum temperature (x, in °F) and ice cr

Rainfall and Crop Yield

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

River Pollution Levels and Industrial Activity

An environmental scientist is investigating whether the level of industrial activity along a river (

Sleep Hours and Reaction Time

A psychology experiment studies the effect of sleep duration (in hours) on reaction time (in millise

Social Media Engagement and Online Sales

An e-commerce company investigates the relationship between daily social media engagement (measured

Speed and Fuel Efficiency

A study examines the relationship between vehicle speed ($$x$$, in mph) and fuel efficiency ($$y$$,

Student Performance and Study Hours

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

Technology Training and Productivity

A technology company wants to know if the number of training hours (x) influences employee productiv

Temperature and Ice Cream Truck Sales

An ice cream truck owner analyzes the relationship between the daily temperature (x, in °F) and ice

Urban vs Rural Pollution Levels

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