AP Statistics FRQ Room

Advertising Campaigns and New Customer Sign-ups

A company ran two advertising campaigns to increase new customer sign-ups. In Campaign 1, there were

Almond Packet Weight Confidence Interval

A quality control team at an almond packaging company wants to estimate the mean weight of its packe

Basketball Free Throw Percentage Confidence Interval

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

Charitable Donation Timing by Age Group

A charity collected data on donation timings (Morning, Afternoon, Evening) and donor age group (Youn

Comparing Sampling Distributions from Populations with Different Variances

Two independent populations have identical means but different variances: Population X has $$\sigma^

Comparing Sleep Hours: High School vs College

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

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 Ratings for Two Products

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

Customer Satisfaction in Two Regions

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

Dietary Preferences by Gender

A survey collected responses from 270 individuals regarding their dietary preference (Vegetarian, No

Digital vs. Traditional Lesson Impact on Class Attendance

A school district is testing whether interactive digital lessons lead to higher class attendance tha

Effect of Exercise Duration on Heart Rate

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

Effect of Fertilizer Types on Tomato Yield

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

Effects of Adding a Constant on Measures of Spread

Consider the dataset of exam scores: {65, 70, 75, 80, 85}. Answer the following:

Evaluating a Histogram for Skewness in Temperature Data

A histogram shows the distribution of daily temperatures (in °F) during a summer month. The histogra

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

Exploring Daily Sales Data Using a Stem-and-Leaf Plot

A small business has recorded its daily sales (in dollars) over 15 days. The data are summarized in

Home Run Distance Analysis

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

Impact of Outliers on Measures of Center

Two datasets represent the annual household incomes (in thousands of dollars) in two similar neighbo

Interpreting a Dot Plot of Daily Coffee Consumption

A dot plot summarizes the number of cups of coffee consumed per day by individuals in a small office

Investigative Task: Evaluating a School Breakfast Program

A school district is considering a breakfast program aimed at improving student performance. Prelimi

Lottery Ticket Analysis

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

NBA Team Wins: Distribution Assessment

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

Normal Distribution: Taxi Mileage

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

Online Shopping Preference by Age Group

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

Political Polling: Candidate Preference

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

Quality Control in Manufacturing

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

Restaurant Preference and Time Slot

A survey of 200 diners asked about their restaurant choice (Restaurant A or Restaurant B) and the ti

Restaurant Wait Time Analysis

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

Simulation and Transformation Effects on the Sampling Distribution

A researcher studying bacterial growth rates, which follow an exponential distribution, collects dat

Sports Performance: Basketball Free Throws

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

Stock Price Outlier Analysis

Consider the summarized daily stock prices (in dollars) of a company given by the following five-num

Stock Price Trends Through Parallel Boxplots

A series of parallel boxplots shows the daily price fluctuations of a particular stock over a 5-year

Studying Daily Step Counts from a Fitness App

A fitness app recorded the number of steps taken per day by its users. The data were grouped into th

Test Scores Histogram Interpretation

A histogram displays the distribution of test scores for an exam. The test score intervals and corre

Analyzing Temperature Effects on Electricity Consumption

A utility company collected data on average daily temperature (in °F) and electricity consumption (i

Assessing Scatterplot Patterns: Nonlinear Relationships

A health study investigates the relationship between the number of hours of exercise per week (X) an

Athletic Performance Correlation Analysis

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

Attendance and Test Performance

A teacher collected data from 25 classes on average class attendance (in %) and average test scores

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 Drink Preference

A survey at a coffee shop collected responses from 120 customers regarding two categorical variables

Comparing Marginal and Conditional Distributions in a Two-Way Table

A car dealership survey recorded data on car color and type. The dealership is interested in the dis

Contingency Table Analysis: Cuteness Factor Study

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

Customer Return Rates for Two Brands

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

Effects of Dropping a High-Leverage Observation

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

Employee Training Effectiveness

A company evaluated the effectiveness of two training methods by measuring subsequent job performanc

Evaluating Sales Team Performance

A sales manager analyzes her team's performance by studying the relationship between years of experi

Exercise and Stress Investigation

A health research team collected data from 40 adults regarding their weekly exercise hours (quantita

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

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

Fitness Tracker: Step Count vs Active Minutes

A fitness tracking app collected data from 50 users on daily step count (in thousands) and active mi

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

Neighborhood Safety Survey

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

Pharmaceutical Dosage Testing

A pharmaceutical company produces tablets designed to contain an active ingredient with a prescribed

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

Relationship between Advertising Spend and Sales

A company examines the effect of advertising spend (in thousands of dollars) on product sales (in th

Relationship between Study Hours and Test Scores

A study investigates the relationship between the number of hours students study per week and their

Residual Analysis and Outlier Detection in a Weight Loss Study

A weight loss program is evaluated by predicting weight loss (in pounds) using a regression model ba

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 Store: Age and Spending Patterns

A retail chain studied the spending patterns of 50 customers. The summary statistics are: mean age =

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

Sampling Distribution of the Sample Range and Its Limitations via Simulation

A statistician is interested in exploring the sampling distribution of the sample range from a bivar

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

Social Media Engagement Analysis

A study examines the relationship between the number of posts an individual makes per day (x) and th

Specialty Coffee Orders at a Coffee Shop

At a coffee shop, 25% of customers order a specialty coffee. In a random sample of $$60$$ customers,

Study Techniques and Exam Performance

A researcher collected data on the number of hours college students spent using active study techniq

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

Agricultural Practices and Crop Yields

Farmers are considering an innovative agricultural practice that may increase crop yields. An observ

Assessing Sampling Techniques in Market Research for a New Product

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

Assessing 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 and Coffee Consumption

In a certain region, the average daily coffee consumption is 3 cups with a standard deviation of 1 c

Comparing Treatment Efficacy in a Retrospective Study

A retrospective observational study was conducted to examine the efficacy of two treatments for a pa

Comparing Two Sample Means in Drug Recovery

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

Customer Satisfaction and Purchase Frequency: An Inference Study

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

Diet, Weight Loss, and Regression Analysis

A nutritionist is studying the relationship between daily caloric intake (Calories) and observed wei

Employee Job Satisfaction Survey

A company surveyed employees across three departments (Sales, HR, IT) regarding their job satisfacti

Evaluating the Effectiveness of a New Drug

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

Evaluating the Sampling Frame in an Urban Survey

A research team plans to survey residents of a large urban area on community services. They initiall

Impact of Undercoverage Bias in Voter Surveys

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

Integrating Surveys and Observational Studies in Urban Environmental Research

An urban environmental research team is investigating the relationship between urban tree cover and

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 Data Variability in Statewide Math Test Scores

A state education board uses multiple samples to estimate average math test scores across high schoo

Investigating Sampling Bias in a Voluntary Response Survey on Social Media Usage

A market research firm conducts an online survey where participants voluntarily respond to questions

Measurement Reliability in Climate Data Collection

A climate study collects rainfall data from multiple sensors distributed across a region. The sensor

Online Ad Click-Through Rates and Sampling Distributions

An online advertising campaign has a click-through rate of 5%, and a webpage receives 500 visitors i

Remote Learning and Student Engagement

A school district wants to evaluate the effectiveness of remote learning on student engagement. Data

Replication in Experimental Designs: Water Purification Study

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

Retrospective Versus Prospective Public Health Studies

A public health agency is planning to study the spread of a novel pathogen. They have access to exte

Simulating Sampling Distributions for Quality Control in Manufacturing

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

Simulating the 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

Simulating the Sampling Distribution from a Skewed Distribution

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

Smartphone Usage and Sleep Quality

Examine the relationship between smartphone usage and sleep quality among college students. Research

Stratified Sampling in an Educational Survey

A school district consists of three types of schools: elementary (40%), middle (30%), and high schoo

Use of Public Transport vs. Car Ownership

A transportation study categorized individuals by region (Urban, Suburban, Rural) and their car owne

Weather Patterns and Traffic Accidents

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

AP Exam Score Distribution: Cumulative Probability Analysis

The table below shows the percentage of students achieving each AP exam score for a given year.

Assessing the Impact of a New Advertisement Campaign

A retail company wants to measure the effect of a new advertisement campaign on store sales. A sampl

Casino Free Chips: Pooling Strategies

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

Coffee Consumption and Alertness Level Regression Analysis

A study examines the influence of coffee consumption (number of cups per day) on an individual's ale

Coin Flip Game Strategies

In a game show, contestants face two different coin flip challenges. In Challenge A, you win if the

Comparing Consumer Spending at Two Malls

Two shopping malls record the average spending per visitor. Mall A has a sample of 100 visitors with

Comparing Daily Sales between Two Store Locations

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

Consumer Product Preference Analysis

A company surveyed 500 consumers about their preference for a new product. The results are summarize

Cumulative Probability Distribution in AP Exam Scores

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

Customer Retention and Marketing Strategies

A company tested two marketing strategies to improve customer retention. Strategy 1 retained 240 out

Defective Products in Quality Control (Binomial Distribution)

In a quality control process, each product has a defect probability of 0.08 and is inspected indepen

Drug Effectiveness Study

Researchers conducted a clinical trial comparing a new drug to a placebo. The recovery outcomes are

Effect of Fertilizer Type on Plant Growth

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

Effects of Outliers on Sampling Distributions

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

Energy Consumption Random Variables

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

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: Encountering an Honest Man

In a certain ancient society, the probability that a randomly selected man is honest is $$0.12$$. As

Hospital ER Wait Times

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

Online Learning vs. Traditional Classroom Formats

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

Online Shopping Behavior by Time of Visit

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

Predicting Blood Glucose from Hemoglobin A1c Levels

A study examines the relationship between Hemoglobin A1c levels (in %) and blood glucose (in mg/dL)

Restaurant Tip Percentage Analysis

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

Sampling Distribution from a Triangular Population

A simulation is performed where samples are drawn from a triangular distribution defined on the inte

TV Advertising and Product Demand Regression Analysis

A company analyzes the relationship between TV advertising spending (in thousand dollars) and produc

University Dining Hall Food Quality Survey

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

Urban Traffic Volume and Air Quality Regression Analysis

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

Voting Behavior in Local Elections

A local election study collected data on voting behavior by political ideology. The summary is as fo

Website Session Duration Analysis

A tech company is analyzing website usage and wants to estimate the typical duration of user session

Analyzing Daily Coffee Sales Sampling Distribution

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

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

Bacterial Count in Water Samples

A water quality test measures the concentration of bacteria (in CFU per 100 ml) in a river. The popu

Battery Lifespan Analysis

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

Central Limit Theorem in Action: Distribution of Household Incomes

In a large metropolitan area, household incomes are highly skewed. A research team takes repeated ra

Comparing Biased Estimators via Simulation Outcomes

A simulation study compares two estimators for a population parameter. Estimator A has a constant bi

Consumer Preferences for Soft Drinks

A market research firm collected data on consumer satisfaction for three soft drink brands. The tabl

Difference in Sample Means: Genetic Mutations and Parental Age

Research indicates that 40-year-old men contribute an average of $$65$$ genetic mutations to their c

Difference in Sample Proportions: Restaurant Experiment

In an experiment to study the effects of environment on eating habits, scientists revamped one of tw

Effect of Ambient Music on Restaurant Wait Times

A study examines the effect of ambient music on restaurant wait times. In a restaurant that plays am

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

Evaluating Math Anxiety and Brain Activity

Research estimates that 80% of individuals with high math anxiety exhibit brain activity consistent

Impact of Devices on Online Purchases

A study on online shopping examines whether the type of device used (Mobile or Desktop) is related t

Lightbulb Life Expectancy Analysis

A certain brand of lightbulbs has a life expectancy that is approximately normally distributed with

Naked Mole Rat Life Expectancy Study

Naked mole rats have a life expectancy that is approximately normally distributed with a mean of $$2

Social Media Usage by Age Group

A survey examined the social media usage intensity among different age groups. The table below categ

Social Media Use and Sleep Duration

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

Student Performance and Study Techniques

A study compared two study methods: using flashcards versus summarization. In the flashcards group (

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 TI-84 for Z-Score Calculations in Sampling Distributions

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

Website Load Time Evaluation

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

Analysis of Survey Data on Online Learning

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

Analyzing Proportions as a Function of Batch Size

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

Confidence Interval for Difference in Proportions: Homeowners vs. Renters on Energy Efficiency

A survey was conducted to compare the preference for energy efficiency improvements between homeowne

Customer Satisfaction: In-Store vs. Online Shoppers

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

Evaluating Trends in Graduation Rates

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

Extremely High Support Rate Survey Analysis

In a survey of 500 voters, 485 express support for a new measure, resulting in a very high sample pr

Hospital Infection Rates: Hypothesis Testing

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

Medical Study: Prevalence of a Risk Factor

A public health survey was conducted to determine the prevalence of a certain risk factor. In a simp

Product Defect Rates in Manufacturing

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

R&D Investment Success Rate

Two companies are comparing the success rates of their R&D investments. Company X had 100 projects w

Reading Program Impact Study

A school district is testing a new reading program designed to improve students' reading proficiency

Recreational Activities and Injury Rates

A health study compared injury rates for participants in contact sports versus non-contact sports. I

Service Reliability Study Analysis

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

Smoking Status and Respiratory Illness

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

Social Media Engagement: Effect of Advertisement on Conversion

An online advertisement campaign tested two different ad designs. For Ad 1, out of 400 views, 80 res

Social Media Usage by Gender

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

Study Habits and Course Success

A professor surveyed 200 students regarding their study habits and exam performance. It was found th

Testing for a Rare Event Proportion

An environmental study collected 1000 water samples to test for a rare pollutant. Only 4 samples tes

University Enrollment Statistics

A university collected enrollment data to compare the study mode (Full-time vs. Part-time) of Domest

Vaccine Acceptance Rates

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

Voter Preference by Region

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

Air Conditioning Energy Consumption

A manufacturer claims that its new air conditioning unit uses on average 6.5 kilowatts of electricit

Air Quality Measurements: Urban vs. Rural

An environmental scientist is interested in comparing the air quality between an urban area and a ru

Average Daily Reading Time of Students

A study investigates the daily reading habits of a group of students. In a random sample of 30 stude

Average Household Electricity Usage

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

Caffeine Consumption and Reaction Times

A study aims to determine whether the consumption of caffeine affects reaction times. Two independen

Comparing Average Wait Times at Two Coffee Chains

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

Comparing Teaching Methods via Test Scores

A school is comparing two teaching methods. In a study, 30 students using Method A had an average te

Comparing Two Diets

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

Enzyme Activity Confidence Interval

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

Evaluation of New Teaching Method Using Paired Data

An educational researcher investigates the impact of a new teaching method on student performance. A

Paired Analysis of Blood Glucose Levels Before and After a Meal

A nutritionist is interested in the effect of a meal on blood glucose levels. Ten participants have

Paired Data in Pre-Test and Post-Test Scores

A company runs a training program and measures employee performance before and after the program. Fo

Paired SAT Score Improvement

An SAT prep course reports that its students improved their scores. In a sample of 30 students, the

Public Transportation Use and Environmental Awareness

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

Randomized Field Experiment on Stress Reduction

A research team is interested in determining whether a mindfulness training program reduces stress l

Response Time in a Virtual Reality Task

A technology company is testing a new virtual reality (VR) system for gaming. They measure the respo

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 the Sampling Distribution for Mean Internet Connection Speeds

An internet service provider uses a simulation to assess the sampling distribution of average speeds

Simulation of the Sampling Distribution for Mean Salary

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

Sodium Intake and Systolic Blood Pressure Analysis

The scatterplot below shows data on individuals' daily sodium intake (in mg, x-axis) and their systo

Training Hours and Employee Productivity Analysis

The scatterplot below shows data on training hours (x-axis) and employee productivity, measured in u

Training Program Performance Improvement

A sports coach is evaluating a new training program by measuring athletes’ performance times before

Yearly Comparison of Mathematics Test Scores

A school wishes to compare average mathematics test scores between two academic years. The data is s

Analysis of Product Defects in a Manufacturing Process

A manufacturing process produces parts that can fall into one of four categories based on defect typ

Book Genre Popularity Study

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

College Major vs Gender: Chi-Square Test for Independence

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

Computer Usage and Major Association Independence Test

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

Customer Satisfaction Across Regions

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

Customer Service Feedback in Retail Stores: Homogeneity Test

A retail chain surveys customer feedback from three stores. Feedback is classified as Positive, Neut

Drug Side Effects Analysis: Chi-Square Test for Independence

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

Exercise Frequency and Music Preference – Chi-Square Test for Independence

A gym surveyed 150 members to study the relationship between exercise frequency (categorized as Low,

Extracurricular Participation and Academic Performance Independence Test

A survey of high school students collected data on extracurricular activity participation (Yes, No)

FRQ 10: Impact of Marketing Strategy on Product Sales

A company implements a new marketing strategy and wants to determine if the acceptance rate of its p

FRQ 20: Investigative Task - Evaluating the Effectiveness of a Public Health Intervention

A public health department implemented an intensive smoking cessation program aimed at reducing resp

Homogeneity in Patient Recovery Rates Across Hospitals

Three hospitals recorded recovery outcomes for a specific surgery. The outcomes are categorized as S

Library Membership and Age

A library survey examines whether there is an association between age group and type of membership (

Major Distribution Across Colleges Goodness-of-Fit Test

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

Observations of Wildlife Distribution

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

Pet Ownership and Residence Type Independence Test

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

Production Line Defect Rates Homogeneity Test

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

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

Shopping Preferences: Homogeneity Test Across Regions

A retail chain surveyed customers in four regions on their preferred shopping mode: In-store or Onli

Simulated Chi-Square Distribution for Voting Patterns

A simulation study is conducted to examine the chi-square distribution under the null hypothesis tha

Sports Participation and Gender – Chi-Square Test for Independence

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

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

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

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

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

Transportation Mode Among City Residents

A city survey examines the relationship between type of residence (Urban vs. Suburban) and preferred

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

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

Voting Behavior and Demographics

A survey collected responses from 700 voters regarding their political affiliation (Democrat, Republ

Workplace Safety Compliance

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

Advertising Budget and Sales Revenue

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

Advertising Impact on Sales

A retail company examines how daily advertising expenditure (in thousands of dollars) influences dai

Age and Reaction Time Study

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

Agricultural Yield Analysis

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

Bicycle Speed vs Oxygen Consumption

A sports scientist is studying how bicycle speed (in mph) affects oxygen consumption (in ml/min) for

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

Climate Change: CO2 Concentration vs Global Temperature Simulation

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

Clinical Trial Dosage-Response Simulation

A medical researcher investigates the relationship between the dosage of a new medication (in mg) an

Effect of Experience on Salary

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

Electricity Usage and Temperature

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

Employee Performance from Experience

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

Energy Consumption and Outdoor Temperature

A study on 30 households examined the relationship between outdoor temperature (x, in °F) and energy

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

Researchers are studying the impact of pollutant concentration (in parts per million, ppm) on the ra

Evaluating the Impact of Work Experience on Promotion Rate

An organizational study examines whether years of work experience (x) affect the promotion rate (y,

Exam Scores vs Hours Studied

A study collected data on the number of hours studied (x) and exam score (y) for 20 students. A scat

Exercise Duration and Heart Rate Recovery

A fitness researcher examines the effect of exercise duration (in minutes) on heart rate recovery ti

Exercise Time and Calorie Burn

A fitness app tracks the number of minutes spent exercising (x) and the number of calories burned (y

Fertilizer Use and Crop Yield

An agricultural researcher studies the effect of fertilizer use ($$x$$, in kg/ha) on crop yield ($$y

Fitness Tracker Study: Daily Steps and Weight Change

A fitness study examined whether daily steps (x, in thousands) predict weekly weight change (y, in p

Food Intake and Weight Gain in Mice

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

Impact of Workout Hours on Body Fat Percentage

A fitness study collected data on the number of hours individuals work out per week (x) and their bo

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

Modeling Blood Pressure Response to Medication Dosage

A medical study investigates the effect of medication dosage (x, in mg) on the reduction in systolic

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

Relationship Between Stress Level and Reaction Time

A psychological experiment collected data on stress levels (x, on a scale of 0-100) and reaction tim

Social Media Influence on Product Sales Simulation

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

Temperature and Electricity Usage

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

Temperature Effects on Motor Speed

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

Urban vs Rural Pollution Levels

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

Water Usage and Crop Yield

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

Wind Speed vs Power Output

An energy analyst is exploring the effect of wind speed (in m/s) on the power output (in kilowatts)

Years of Experience and Salary Increase

A study investigated the relationship between years of job experience (x) and annual salary (in thou