AP Statistics FRQ Room

Analysis of Categorical Data from Elections

A recent survey sampled 1000 voters to determine their preferred candidate in a local election. The

AP Music Tastes Survey

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

Blood Pressure Analysis in Clinical Trial

A clinical trial studying a new treatment records the blood pressure of 19 patients. The sample has

Car Price and Mileage Regression Analysis

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

Comparing Cumulative Frequency Graphs for Age Distributions

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

Comparing Exam Score Distributions

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

Comparing Sleep Hours: High School vs College

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

Customer Ratings for Two Products

A market research firm collected customer ratings for two competing products. In a survey, 250 out o

Customer Satisfaction in Retail Chain

A retail chain surveyed 250 customers regarding their satisfaction level (Satisfied, Neutral, Dissat

Effect of Constant Adjustments on Mean Salary

Consider the salaries (in dollars) of six employees given below: $3,000; $7,000; $15,000; $22,000; $

Empirical Rule Verification via Simulation

A professor is studying exam scores that are normally distributed with a mean of 70 and a standard d

Employee Salary Adjustments

A company’s six employee salaries (in dollars) are as follows: {3000, 7000, 15000, 22000, 23000, 380

Error Rates in Two Production Machines

A factory operates two machines that produce the same part. Machine A produced 300 parts with 12 def

Examining Non-Response Bias in Mail Surveys

Two separate mail surveys were conducted in different regions. In Region X, 150 out of 300 surveys w

Home Run Distances in Ballparks

The following set of home run distances (in feet) to center field in 13 ballparks is given: {387, 40

Home Run Distances: Mean, Median, and Outlier Impact

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

Internet Usage Among College Students

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

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

NBA Team Wins: Distribution Assessment

The numbers of wins for NBA teams in two conferences are summarized using comparative data displays.

Normal Distribution of Taxi Mileage

Taxicabs in a city are driven an average of $$75000$$ miles per year with a standard deviation of $$

Online Course Satisfaction Hypothesis Test

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

Online vs. In-Person Instruction on Language Course Retention

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

Quality Control in Manufacturing

A quality control inspector examines items on an assembly line. Each item has a 2% chance of being d

Residual Analysis: Car Efficiency versus Engine Size

A study investigates the relationship between engine size (in liters) and fuel efficiency (in miles

Sampling Distribution and Confidence Interval Implications for Household Incomes

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

School Year Length Preferences Survey

A survey is conducted among 2000 parents regarding their preferred school year length. The frequency

Simulated Sampling Distribution of the Standard Deviation

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

Stemplot Construction: Analyzing a Data Set

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

Student Major and Internship Status

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

Subway Train Arrival Times

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

Vehicle Type and Fuel Preference

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

Website Traffic: Click-Through Rate

An online advertisement is viewed by 250 visitors. Each visitor clicks the ad with a probability of

Advertising Campaign and Sales Analysis

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

Analysis of Two Categorical Variables in a School Survey

A high school surveyed 300 students to determine their favorite subject (Mathematics, Science, or En

Chi-Square Analysis for Dietary Habits and Exercise Frequency

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

Comparing Two Regression Models for Chlorophyll Content Prediction

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

Complex Survey Analysis: Income and Expenditure Patterns

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

Customer Satisfaction and Purchase Frequency

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

Effectiveness of a New Curriculum

A school district implemented a new curriculum in some of its schools and maintained the traditional

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 Coefficient of Determination in Athletic Performance

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

Exercise and Resting Heart Rate

In a health study of 40 adults, researchers examined the relationship between daily exercise duratio

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

Geometric Distribution of Quick Transactions at a Bank

At a bank teller, the probability that a customer completes a transaction in less than 5 minutes is

Housing Prices and Square Footage Analysis

A real estate analyst collected data on various houses regarding their square footage (in square fee

Housing Renovation Impact on Property Values

A real estate researcher is investigating whether the cost of home renovations (x, in thousands of d

Impact of Caffeine Intake on Reaction Time

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

Impact of Study Methods on Test Performance

A university is interested in determining the effect of different study methods on students' perform

Inference on the Slope of Study Hours vs. Exam Score

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

Medical Test Accuracy and Disease Prevalence

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

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

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 Fitness Improvement from Exercise Duration

A fitness study examined the relationship between the daily exercise duration (x, in minutes) and th

Regression Analysis of Movie Attendance and Concession Sales

A movie theater records daily attendance (x) and the number of concession sales (y, measured in hund

Restaurant Order Survey

A restaurant surveyed 140 customers to see if there was any association between meal type (Vegetaria

Sampling Distribution of Exam Scores

Exam scores at a college are normally distributed with a mean of $$75$$ and a standard deviation of

Simulating the Sampling Distribution of the Sample Mean in Bivariate Data

A study collects data on the number of study hours (x) and exam scores (y) for 100 students. Researc

Simulation of the Mean Residuals in a Regression Model

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

Sports Performance: Height vs. Weight Analysis

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

Study Habits and Exam Scores: Regression Inference

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

Study Hours and Exam Scores

A high school collected data on the number of hours students studied for an exam (x) and their corre

Wait Time and Meal Satisfaction

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

Warehouse Shipping Times

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

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

Workforce Diversity Study

A corporation conducted a study to analyze the distribution of employees across different job levels

Analysis of Recycling Behavior

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

Analyzing Store Price Data

A retail chain claims that the average price of a particular product is at most \($10\). To test thi

Analyzing Student Study Habits

A high school conducted a study comparing student performance based on their method of studying. The

Cluster Sampling in Educational Research

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

Cluster Sampling in Educational Testing

A school district with 50 schools wants to evaluate a new teaching method. They decide to randomly s

Community Fitness Program and Weight Loss

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

Comparing Disease Incidence in Two Regions

A public health study investigated the incidence of a particular disease in two regions. In Region A

Comprehensive Analysis of Consumer Behavior in Response to Online Advertisements

A consumer goods company wants to study how online advertisements influence purchasing behavior. The

Customer Loyalty Programs: New vs. Established Store

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

Data Collection in a Prospective Observational Study

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

Designing a Double-Blind Experiment for a New Drug

A pharmaceutical company intends to test a new drug aimed at reducing blood pressure. To eliminate b

Effect of Diet on Cholesterol Levels

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

Effect of Noise Levels on Sleep Quality

An environmental study investigates the association between ambient noise level (in decibels, x) and

Evaluating Bias in a Sampling Process: Voluntary Survey

A city council conducts a voluntary online survey regarding community safety. Out of 150 responses,

Evaluating Survey Sampling Methods

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

Hypergeometric Distribution in Quality Inspection

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

Manufacturing Processes and Product Lifespan

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

Music Therapy and Stress Levels

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

Prospective Cohort Study for Diabetes and Lifestyle Factors

A health organization plans to conduct a prospective cohort study to investigate how lifestyle facto

Remote Learning Effectiveness

At a high school, the impact of transitioning to remote learning on student test scores is studied u

Replication in Experimental Designs: Water Purification Study

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Scatterplot Analysis and Regression Line Interpretation

A researcher investigates the relationship between the number of hours studied (x) and exam scores (

Simulating Cluster Sampling and its Effects on the Sampling Distribution

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

Simulating the Effect of Sample Size on Standard Errors

A study is performed using simulation to assess how sample size affects the standard error of the sa

Simulation of the Sampling Distribution of Proportions in Quality Testing

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

Systematic Sampling in a Traffic Accident Study

A city transportation department wants to assess the frequency of traffic accidents at intersections

Traffic Flow Analysis

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

Car Purchase Decisions by Region

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

Comparing Patient Wait Times at Two Clinics

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

Customer Satisfaction Survey

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

Defects from Two Machines

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

Evaluating a New Teaching Technique in High School

A school district is testing a new interactive teaching technique against the traditional method. Ce

Game of Score Sums

Two friends play a game where Friend A draws a card with values {2, 4, 6} (each equally likely) and

High School SAT Scores Analysis

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

Highway Construction Productivity Analysis

The daily output of highway construction (in miles) depends on weather conditions as follows: | Wea

Hospital ER Wait Times

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

Impact of Study Habits on Test Scores

A teacher wants to examine if spending an extra 30 minutes reviewing material after class influences

Insurance Policy Sales Analysis

An insurance salesperson records her daily sales of auto and home insurance policies. The probabilit

Online Shopping Behavior by Time of Visit

An e-commerce website collected data on visitor behavior during different times of the day. The tabl

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

Reading Preferences by Genre and Format

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

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

Scatterplot Regression Analysis on Advertising and Sales

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

Simulated Distribution of Sample Proportions with a Biased Coin

A simulation uses a biased coin with a probability of heads $$p = 0.8$$. In each simulation run, the

Simulated Sampling Distribution for a Binomial Variable with Larger n

A simulation is executed where 50 independent Bernoulli trials with probability $$p = 0.4$$ are perf

Simulation of the Law of Large Numbers in Practice

A simulation is conducted using a biased die that shows a '6' with a probability of $$0.7$$. The die

Small Business Daily Revenue Analysis

A small business tracked its daily revenue over a period of 30 days. The sample mean daily revenue w

Transformation of Payout Values

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

Virus Spread Modeling among Animal Species

A study examines the spread of a virus among three animal species with the following data: | Specie

Analyzing Differences in Means Between Two Machines

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

Applicability of the Central Limit Theorem for Skewed Data

Consider a population with a heavily right-skewed distribution having a mean of $$\mu=50$$ and a sta

Assessing the Conditions for the Central Limit Theorem

A production facility records the number of widgets produced per day by a machine. The daily product

Battery Life Analysis Using Normal Distribution

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

Battery Lifespan Analysis

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

Caffeine Content Analysis

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

Coffee Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Juice Bottling Process

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

Difference in Sample Proportions: Revamped vs. Unrevamped Restaurant

A study compares customer behavior at two restaurants. At a revamped restaurant, 30% of a sample of

Effect of Sample Size on Variability

In a manufacturing process, the diameters of bearings are measured. Individual measurements have a s

Employment Benefits Perception

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

Estimator Evaluation in Baseball Manufacturing

In a quality control study for manufacturing professional baseballs (true mean weight = $$146$$ gram

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

In a survey, it is found that 40% of respondents own a smartphone. A random sample of 200 respondent

Financial Returns: Biased vs. Unbiased Estimators

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

Hospital Patient Satisfaction by Department

A hospital surveyed patient satisfaction in three departments. The table below displays the number o

Hypothesis Testing for a New Drug's Effect on Blood Pressure

A clinical trial is conducted to test the claim that a new drug reduces blood pressure by 10 mmHg. I

Impact of Sample Size on the Standard Error

Researchers are investigating how sample size affects the variability of the sample mean. From a pop

Naked Mole Rat Life Expectancy

The life expectancy of naked mole rats is normally distributed with a mean of $$\mu = 21$$ years and

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

Prediction Intervals in Regression Analysis

A regression analysis is performed to predict final exam scores based on study hours. The regression

Quality Control in Manufacturing: Sampling Distribution of Mean Weight

A factory produces metal rods with a mean weight of $$100$$ grams and a standard deviation of $$5$$

Quality Control of Production Errors

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

Sample Proportion Variability in Customer Preference Studies

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

Sampling Distribution for Differences in Sample Proportions in Political Polling

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

Sampling Distribution for Differences in Sample Proportions: Political Polls

An exit poll surveys two candidates. Candidate X receives support of 48% from a sample of 400 voters

Sampling Distribution of Proportions: Defective Products

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

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

Survey on Policy Support in Two Regions

A survey was conducted in two regions regarding support for a new public policy. In Region A, out of

Using invNorm in Sampling Distributions: Statistical Thresholds

Scores on a standardized test are normally distributed with a mean of $$\mu = 500$$ and a standard d

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

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

Epidemiology Study: Difference in Disease Incidence

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

Estimating Customer Satisfaction

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

Evaluating a Policy Change via Proportion Hypothesis Testing

A city government wants to evaluate the impact of a new traffic safety policy. Before the policy, in

Gender Differences in Product Preference

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

Healthcare Plan Satisfaction

A survey was conducted among employees to assess satisfaction with their healthcare plans. Participa

Hospital Infection Rates: Hypothesis Testing

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

Impact of a New Regulation

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

Measuring Customer Preferences

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

Political Polling: Estimating Voter Support

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

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

Salon Customer Satisfaction: Confidence Interval Analysis

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

Sample Size Determination for Desired Margin of Error

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

Sampling Distribution and Confidence Intervals for Proportions

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

School Intervention Study

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

Simulation and Analysis for Rare Diseases

An epidemiologist is studying a rare disease with an estimated prevalence of 0.5%. They simulate dra

Social Media Campaign Engagement Analysis

A company runs a social media campaign aiming for a target engagement rate of 40%. In a sample of 60

Social Media Usage Among Age Groups

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

Sports Participation by Gender and Sport Type

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

Urban vs. Rural: Survey on Public Transportation Usage

A survey was conducted to compare the use of public transportation between urban and rural residents

Voter Turnout Behavior Survey

A political organization implements a get-out-the-vote campaign in several precincts and wishes to d

Accident Rates Comparison Between Departments

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

Analysis of Weekly Exercise Duration

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

Battery Life Study

A battery manufacturer claims that the new battery model has an average lifespan of $$\mu$$ hours. A

Change in Manufacturing Process: Product Lifespan

A manufacturing company claims that a new manufacturing process increases the lifespan of its produc

Coffee Shop Wait Times

An urban coffee shop is interested in assessing its average customer wait time (in minutes) from pla

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

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

Daily Steps: Wearable Device Analysis

A fitness tracker company wishes to estimate the average number of steps taken per day by its users.

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

Effectiveness of Tutoring Program Investigation

A school district is interested in the effectiveness of a new tutoring program on improving student

Employee Training Effectiveness

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

Engine Emissions Compliance

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

Fertilizer Impact on Plant Growth

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

Impact of a Study Program on Exam Performance

A school introduces an intensive study program and measures students' exam scores before and after i

Investigative Analysis of Customer Service Performance Metrics

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

Life Span Analysis of Light Bulbs

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

Production Time and Number of Defects Analysis

The scatterplot below displays data on production time in minutes (x-axis) and the number of defects

Reaction Time Hypothesis Test

A psychologist wishes to test a manufacturer's claim that the average driver reaction time is \(0.8\

Reaction Time One-Sample t-Test

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

Reaction Time Testing Under Caffeine Effects

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

SAT Preparation Class Improvement

A tutor runs an SAT preparation class with 25 students. The differences between the post-test and pr

Simulation of the Sampling Distribution for Mean Salary

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

Sleep Duration and Reaction Time Analysis

The scatterplot below shows data on hours of sleep (x-axis) and reaction time in seconds (y-axis) fr

Study on Exam Anxiety Reduction

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

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

Academic Majors and Study Habits

A university studies the relationship between a student's major (STEM, Humanities, Social Sciences)

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

Assessing the Fit of a Theoretical Distribution on Emergency Call Durations

Emergency call durations are categorized as Short (0–2 minutes), Medium (2–5 minutes), and Long (ove

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

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

Book Genre Popularity Study

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

Computer Usage and Major Association Independence Test

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

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

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

Distribution of Types of Crimes in a City

A study compares the types of crimes in two districts of a city. District A reported: Property = 80,

Effectiveness of a New Training Program across Branches

A company implements a new training program in three of its branches. After the program, employees a

Fruit Distribution Goodness-of-Fit Test

A fruit vendor claims that the distribution of fruits in a basket follows the percentages: 40% Apple

Game Outcome Distribution

A board game produces three outcomes: win, loss, and draw. The expected probabilities for these outc

Independence Test: Dietary Supplements and Energy Levels

A fitness center surveyed 250 members about their use of dietary supplements (Yes/No) and their self

Insurance Claim Types: Independence Test Across Age Groups

A study examines whether the type of insurance claim (Auto, Home, Health) is associated with age gro

Observations of Wildlife Distribution

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

Preferred Study Methods: Homogeneity Test Across Colleges

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

Production Line Defect Rates Homogeneity Test

A factory operates four production lines, each producing a sample of 200 items. The numbers of defec

Simulating the Distribution of the Chi-Square Statistic

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

Sports Participation by Gender

A school survey collected data on sports participation among students, broken down by gender (Male,

Traffic Light Malfunction Analysis

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

Advertising Expenditure vs Sales

A company investigated the relationship between the amount spent on advertising (in thousands of dol

Advertising Reach and Customer Acquisition

A digital marketing analyst studies the relationship between the number of advertising impressions (

Car Fuel Efficiency and Car Weight Regression Analysis

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

Consumer Spending and Income Levels

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

Effect of Class Size on Student Achievement

An education researcher examines data from 50 classrooms to study the relationship between class siz

Effectiveness of a New Drug on Blood Pressure

A pharmaceutical company is investigating whether a new drug reduces blood pressure as the dosage (i

Electricity Usage and Temperature

An energy analyst examines how average daily temperature (x, in °F) affects household electricity us

Employee Performance and Training Hours

A company is assessing employee performance scores (out of 100) based on the number of training hour

Engineering: Stress and Strain in Alloys

In an experiment studying a new alloy, engineers measured stress (x, in MPa) and strain (y, dimensio

Environmental Pollution and Distance Simulation

An environmental scientist is investigating how the concentration of a pollutant (in ppm) changes wi

Exercise Duration and Weight Loss

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

Food Intake and Weight Gain in Mice

In an experiment with mice, researchers study the relationship between daily calorie intake ($$x$$)

Height and Weight Relationship: Male vs Female

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

Hours of Training and Athletic Performance

A sports scientist examines the relationship between hours of training per week ($$x$$) and athletic

Housing Price Estimation

A real estate analyst examines the relationship between the age of a house (in years) and its price

Housing Prices Prediction

A real-estate analyst investigates how the selling price of houses relates to their size (in square

Ice Cream Sales vs Temperature

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

Internet Speed and Streaming Buffer Time

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

Machine Operating Time and Defect Rate

A manufacturing plant collected data to investigate the relationship between machine operating time

Manufacturing Process Optimization

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

Manufacturing Quality Control

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

Marketing Impact: Social Media Activity vs. Product Sales

A company collected data from 45 markets to investigate the effect of social media advertising hours

Marketing Spend and Customer Footfall

A retail company is examining whether there is a relationship between local advertising expenditure

Plant Growth vs Fertilizer Amount

An agronomist is studying the effect of fertilizer amount (in kg/ha) on plant growth (in cm) in a co

Predicting Sales Based on Advertising Budget

A company wants to understand the relationship between its advertising spending (in thousands of dol

Predicting Student Performance with Attendance Rates

A teacher collects data on student attendance rates (x, in percentage) and corresponding performance

Rainfall and Crop Yield

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

Rainfall vs Crop Yield

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

Regression Analysis in Judicial Decisions: Predicting Recidivism Risk Scores

A study uses regression analysis to predict recidivism risk scores based on the number of prior offe

Social Media Influence on Product Sales Simulation

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

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 and Electricity Usage

A utility company is studying the relationship between the average outside temperature (in °F) and t

Traffic Flow Analysis: Regression Slope Simulation

A transportation planner is analyzing the relationship between the number of vehicles on a roadway a

Water Usage and Crop Yield

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

Weather Forecasting: Humidity vs. Chance of Precipitation

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