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 Class Enrollment Analysis

In a school, 300 students were surveyed regarding the number of Advanced Placement (AP) courses they

AP Course Enrollment Among High School Seniors

A survey of 2200 high school seniors collected data on the number of AP classes they are taking. The

Application of the Empirical Rule to IQ Scores

Assume that IQ scores are normally distributed with a mean of $$100$$ and a standard deviation of $$

Comparing Pass Rates for Two Classes

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

Comparing Sampling Distributions from Populations with Different Variances

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

Customer Satisfaction in Retail Chain

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

Daily Step Count Hypothesis Test

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

Distribution Shape and Confidence Interval Interpretation

A survey of 100 car owners reveals that the cars’ mileages have a mean of $$60000$$ miles and a medi

Effect of a Multiplicative Transformation on Distance Data

A group of athletes has their running distances (in kilometers) recorded as: {5, 6, 8, 7, 10, 9}. Th

Effect of Fertilizer Types on Tomato Yield

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

Effects of Linear Transformation on Data

Let a data set $$X$$ have a mean of $$\mu$$ and a standard deviation of $$\sigma$$. Suppose we defin

Employee Salary Adjustments

A company has six employees with the following salaries (in dollars): $$\{3000, 7000, 15000, 22000,

Impact of an Outlier on Summary Statistics

Consider the data set $$\{4, 5, 6, 7, 50\}$$. Answer the following:

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

Investigative Task: Public Park Usage Study

A city park department seeks to understand how weather conditions affect park attendance. They plan

Online Course Satisfaction Hypothesis Test

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

Online Examination Scores

Scores on an online examination are normally distributed with a mean of $$75$$ and a standard deviat

Regression Analysis: Height and Shoe Size in Adolescents

A study on adolescents collected data on height (in cm) and shoe size. The least-squares regression

Relative Frequency Calculation from Pet Ownership Survey

A survey regarding pet ownership in households produced the following frequency table: | Pets Owned

School Year Length Preference Survey Analysis

A survey of 2000 parents was conducted asking their preference for the number of days in the school

Simulated Sampling Distribution of a Sample Proportion for a School Lunch Preference Survey

A school conducts a survey to determine if students prefer the current school lunch or an alternativ

Simulation of the Sampling Distribution of the Mean Number of AP Classes Taken

A study of 2200 high school seniors reports the number of AP classes taken as follows: 0 AP classes

Social Media Platform Usage by Gender

A survey of 400 respondents recorded their preferred social media platform (Platform X or Platform Y

Stock Price Outlier Analysis

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

Study Program Effectiveness Hypothesis Test

A researcher wants to determine if a new study program increases test scores. In a random sample of

Teacher Age Distribution Analysis

The ages (in years) of 12 mathematics teachers are given as follows: {24, 25, 25, 29, 34, 37, 41, 42

Analyzing a Survey on Social Media Use and Sleep

A researcher surveys 100 college students to study the relationship between the number of hours spen

Chi-Square Analysis for Dietary Habits and Exercise Frequency

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

Customer Loyalty Program Analysis

A retail company collected data on the number of store visits (x) by loyalty card members and the po

Customer Return Rates for Two Brands

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

Cuteness Factor Study Revisited

A Japanese study collected data on 250 volunteers who were shown pictures of cute baby animals, adul

Dietary Effects on Blood Pressure

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

Effectiveness of a Medical Treatment

A clinical trial is designed to evaluate the effectiveness of a new cholesterol-lowering drug. Patie

Employee Training Effectiveness

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

Employment Rates of College Graduates

A survey was conducted to compare the employment outcomes of graduates from two colleges. College X

Evaluating Public Health Data on Smoking and Lung Cancer

A study was conducted to investigate the association between smoking and lung cancer incidence among

Exercise and Stress Investigation

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

Green Energy Adoption and Energy Savings

Data from 35 households were analyzed to study the relationship between the percentage of energy fro

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

Predicting Apartment Rents

A real estate company collected data on apartment sizes (in square feet) and their monthly rents (in

Promotion Program Success Comparison

A company implemented two distinct promotional programs to boost sales. In Program 1, 92 out of 150

Restaurant Tip Analysis

In a study of restaurant bills, data were collected on the total bill amount (in dollars) and the ti

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

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,

Startup Revenue Growth

A startup's monthly revenue (in thousands of dollars) is approximately normally distributed with a m

Study Habits and Exam Pass Rates

A researcher compared exam pass rates between two groups of students enrolled in different study pro

Temperature and Ice Cream Sales

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

Wait Time and Meal Satisfaction

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

Agricultural Practices and Crop Yields

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

Analysis of Product Return Rates: Online vs. In-Store

A retailer wants to compare product return rates between online and in-store purchases. Among online

Analyzing Bias in Convenience Sampling at a Mall

A researcher conducts a convenience survey at a local shopping mall to gauge consumer satisfaction w

Bootstrapping the Sampling Distribution of a Mean

A researcher has collected exam scores from 15 students and wishes to estimate the sampling distribu

Comparing Retrospective and Prospective Studies in Outbreak Analysis

An epidemiological study is being designed to investigate factors contributing to a recent influenza

Comparing Test Scores Between Two Teaching Methods

A school is evaluating two different teaching methods. Group A, using Teaching Method A, had 25 stud

Customer Satisfaction with New vs. Old Product

A market research survey was conducted to compare customer satisfaction between a new product and an

Designing a Prospective Study for a Drug Trial

A pharmaceutical company is testing a new drug for lowering blood pressure. The study will involve f

Double-Blind Experiment Design for Nausea Reduction

A research team is testing a new wristband designed to reduce postoperative nausea. To eliminate pla

Environmental Study on Pollution Levels

A retrospective study examined water quality from 40 rivers in a region, measuring the concentration

Estimating Average Park Visit Duration

A study is conducted to assess the average length of time (in minutes) that visitors spend at a loca

Evaluation of a New Teaching Method

An educational study compared a New teaching method with a Traditional one in terms of student exam

Examining Study Habits and Academic Performance

A college conducts a study using stratified sampling among freshmen, sophomores, and juniors to anal

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 Sales Increase

A company wants to evaluate if exposure to an advertising campaign affects the likelihood of an incr

Online Tutoring and Student Performance

A school district implements an online tutoring program aimed at improving student math performance.

Online vs. In-Person Shopping Preferences

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

Predicting Blood Pressure from Age: Regression and Inference

A health researcher is examining the relationship between the age of adults and their systolic blood

Predicting Car Mileage from Engine Size

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

Randomized Block Design in Evaluating a Teaching Method

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

Retail Store Checkout Efficiency Study

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

Simulating Sampling Distributions for Quality Control in Manufacturing

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

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 for a School Survey on Sports Participation

A high school with 500 students wants to survey opinions about sports participation. The principal d

Understanding Sampling Error through Repeated Sampling

A researcher repeatedly draws independent simple random samples of size 50 from a large population w

Volunteer Firefighter Response Times

A prospective study of volunteer firefighter response times records data from 45 incidents. The samp

Voter Behavior: Support for Policy X Among Different Age Groups

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

Voting Preference Analysis

A political analyst collected data on voting preferences by age group. The table below shows the num

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.

Carnival Game of Chance: Payoff Transformations

A carnival game offers different monetary payoffs with the following probabilities: | Payoff ($$\$\

Casino Free Chips Expected Sum

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

Comparing Manufacturing Processes for Defect Reduction

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

Comparing Sampling Distributions Under Different Population Variabilities

A simulation is run for two populations: Population A has a low variance and Population B has a high

Defective Lightbulbs: A Binomial Distribution Problem

A lightbulb has a $$0.1$$ probability of being defective, and the outcomes are independent. Analyze

Employee Training and Department Performance

A company recorded the outcomes of a recent employee training program across three departments. The

Exam Score Cumulative Distribution

The following table displays the distribution of scores on an exam from 200 students:

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

Investment Returns: Sum and Difference of Random Variables

An investor has two independent investments with the following annual return distributions: Investm

Lottery Ticket Expected Outcome

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

Medical Trial for a New Drug

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

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

Reading Preferences by Genre and Format

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

Simulated Sampling Distribution of Survey Proportions

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

Student Exam Score Distribution

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

Student Study Hours and Exam Performance Regression Analysis

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

Student Testing Strategy and Scores Analysis

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

Testing Customer Satisfaction Claims

A coffee shop claims that 80% of its customers are satisfied. To test this claim, a random sample of

Transportation and Work Patterns Survey

A survey of 500 people recorded their preferred mode of transportation and work location (Remote or

Website Session Duration Analysis

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

Analysis of Athletic Performance Improvements

A coach is comparing the performance improvements of athletes following two different training progr

Assessing Variability in a Manufacturing Process

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

Bootstrapping and the Sampling Distribution of the Mean

A researcher collects daily sales data from a small store over 30 days. The observed sample mean is

Caffeine Content Analysis in Energy Drink Boxes

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

Car Engine Performance Analysis

In a quality control study, car engine performance scores are normally distributed with a mean of 90

Central Limit Theorem in Customer Service Times

In a call center, individual call durations are skewed with an average of $$\mu = 5$$ minutes and a

Comparing Drug Efficacy Using Sample Proportions

A clinical trial is conducted to compare the efficacy of a new drug versus a placebo. It is estimate

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

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

Dream Recall Simulation Study

A study on dream recall in college students found that the median number of dreams remembered per ni

Employee Training Program Evaluation

A company evaluated the effectiveness of its training programs by mode of delivery (Online vs. In-Pe

Environmental Study: Tree Heights

A biologist is studying tree heights in a forest. Although individual tree heights are not normally

Evaluating Genetic Mutations in New Fathers

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

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

Favorite Ice Cream Flavor Survey – Sampling Proportions

In a survey on ice cream preferences, past research indicates that approximately 40% of respondents

Music Streaming Service Satisfaction

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

Polling Data Analysis

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

Regional Customer Satisfaction Analysis

A marketing study examines customer satisfaction in two regions. In Region A, the true satisfaction

Sample Size Effects: Simulation Analysis

A simulation study is performed to examine the effect of sample size on the variability of the sampl

Sample Variance Distribution in Produce Weights

A study measures the weights of produce, where the population variance is known to be $$16$$ (kg^2).

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 Sample Proportions in a Survey

A survey indicates that 65% of viewers prefer streaming TV over cable. A random sample of 150 viewer

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

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

Using TI-84 Functions for Normal Probability

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

Voting Behavior by Gender

A political study analyzed voting behavior based on gender. The table below displays the counts of m

Widget Lifespan Quality Control

A factory produces widgets with an average lifespan of $$500$$ hours and a standard deviation of $$2

Analysis of Emergency Room Wait Times Satisfaction

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

Analyzing Voter Turnout Using Confidence Intervals

An exit poll of 800 voters revealed that 560 voted in favor of Candidate Y. Construct a 95% confiden

Blood Donation Campaign Study

A local health department funds two different public campaigns to increase blood donation rates. One

College Acceptance Rate Comparison

Two high schools wish to compare college acceptance rates. School X admitted 75% of its applicants o

Comparative Study on Voter Registration Between Two States

Two neighboring states conducted surveys on voter registration. In State A, 320 out of 400 eligible

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

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

Comprehensive Analysis of Confidence and Significance in Survey Data

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

Consumer Product Hypothesis Test

A company claims that at least 60% of its customers like a new product. To test this claim, a simple

Customer Satisfaction: In-Store vs. Online Shoppers

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

Designing a Survey for Voting Behavior

A political researcher plans to estimate the proportion of voters who will support a particular cand

Digital Platform Success Rate Comparison

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

Drug Efficacy in Clinical Trials

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

Election Poll Margin of Error Analysis

An election poll reports a candidate's support proportion as 0.48 with a margin of error of 0.04 at

Evaluating Strike Support

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

Gender Representation in STEM Fields

A study was conducted to compare gender representation in STEM fields among recent graduates. In a s

Hypothesis Testing and Errors: Sports Performance

A coach claims that at least 70% of his players hit a home run. In a game, 50 players are observed a

Nutrition Labeling Impact Study

A government agency implements a policy requiring prominent nutritional labels on packaged foods. A

Online Advertising Impact Study

An online retailer wishes to study whether exposure to a particular digital advertisement increases

Online Education Satisfaction

A study comparing satisfaction with education methods surveyed two groups. One group of online stude

Power Analysis in Proportion Testing

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

Public Health: Influenza Vaccination Rates

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

Public Health: Smoking Rates by Region

A public health researcher wants to compare smoking rates between two regions. In Region 1, a survey

Quality Control in Manufacturing

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

Sampling Distribution and Confidence Intervals for Proportions

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

School Lunch Program Participation

A study examines participation in school lunch programs in two schools. In School X, 60 out of 150 s

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 Usage Among Age Groups

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

Sports Statistics: Free Throw Confidence Interval

A basketball player's free throw performance is evaluated over 100 attempts, in which he makes 72. A

Survey on Remote Work Satisfaction

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

Traffic Accident Analysis

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

University Enrollment Statistics

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

Accident Rates Comparison Between Departments

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

Average Daily Sales at a Retail Store

A retail manager records the daily sales (in thousands of dollars) over a period of 20 days. The sam

Blood Pressure and Sodium Intake Regression

A study investigates the relationship between daily sodium intake (in mg) and systolic blood pressur

Blood Pressure Reduction Confidence Interval

A clinical trial was conducted to test the effectiveness of a new medication on reducing blood press

Caffeine Consumption and Reaction Times

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

Career Development Program

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

Comparative Analysis of Lecture Techniques Using Paired Data

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

Comparing Two Treatments for Improvement

Two treatments for a health condition were tested. Group A (n = 40) experienced an average improveme

Computer Downtime Analysis

A sales representative suspects that his company's computers have higher average non-operational (do

Customer Satisfaction Survey

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

Diet Program Effectiveness

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

Difference in Accident Rates

In a study of safety in a manufacturing plant, monthly accident data were collected for two independ

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

Effect of Training on Typing Speed: Paired Analysis

A company implemented an intensive typing training program. Typing speeds (in words per minute) were

Employee Training and Productivity Outcome

A company examines whether the type of training (Online vs. In-person) affects employee productivity

Enzyme Activity Confidence Interval

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

Examining Teaching Methods

A school is comparing two teaching methods: Traditional and Modern. Student outcomes are classified

Impact of Variability on Confidence Intervals: A Simulation Study

A simulation study is conducted to explore how differences in sample variability affect the width of

Investigating Student Reaction Times

A psychologist studies the reaction times of 30 college students using a computerized test. The meas

Manufacturer's Claim on Product Weight

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

Paired SAT Score Improvement

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

Pre- and Post-Treatment Blood Pressure

A clinical trial is conducted to assess the effectiveness of a new treatment for lowering blood pres

SAT Preparation Class Improvement

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

Simulation of Sampling Distribution for Average Household Income

An economist is studying household incomes, which are known to be right-skewed. The economist uses s

Simulation of Sampling Distribution in a Clinical Trial

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

Simulation of the Sampling Distribution for Mean Salary

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

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

Social Media Usage Before and After an Intervention

A researcher studies the effect of a digital detox program on daily hours spent on social media. For

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 Performance: Honors vs. Non-Honors

A school is investigating whether there is an association between program type (Honors vs. Non-Honor

Adoption Rates of Electric Vehicles by Region

A study compares the adoption rates of electric vehicles in three different regions: Urban, Suburban

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

Book Genre Popularity Study

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

Candy Flavor Preferences: Goodness-of-Fit Test

A local candy shop claims that customer preferences for its four candy flavors (chocolate, strawberr

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

Dietary Preferences Across Regions

A nutrition study surveyed residents from three cities to determine their dietary preferences: Veget

Fair Dice Rolling Goodness-of-Fit Test

A die is believed to be fair. In 120 rolls, the outcomes were observed as follows: Face 1 = 14, Face

FRQ 5: Health Supplement Side Effects

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

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

Goodness-of-Fit Test in Marketing Campaign Response

A company’s marketing campaign is expected to yield customer reactions in five groups with the follo

Homogeneity in Dietary Habits Across Regions

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

Market Research: Chi-Square Test for Homogeneity of Brand Choices

A market researcher wishes to determine whether consumer brand preference is consistent across three

Online Shopping Day Preferences: Chi-Square Goodness-of-Fit

A retailer surveys 150 online shoppers to determine which day of the week (Monday through Friday) th

Political Polling: Party Affiliation and Issue Stance

A national poll cross-classifies respondents by party affiliation (Democrat, Republican, Independent

Product Defect Rates – Chi-Square Goodness-of-Fit

A quality control engineer hypothesizes that defects in a product occur with equal probability among

Public Opinion on Policy: Chi-Square Test for Independence

A poll surveyed 600 individuals regarding their stance (Support or Oppose) on a new public policy, a

Race Participation in Marathon

A marathon organizer expects the racial participation to follow these percentages: Group 1 = 30%, Gr

Robustness of Chi-Square Test: Small Expected Counts

A survey on elective subject choice among students produced observed counts: Subject A = 25, Subject

Simulated Chi-Square Distribution for Voting Patterns

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

Simulated Data: Random Number Generator Uniformity Test

A random number generator produced 1000 numbers that were binned into 10 equal intervals. The observ

Simulating the Distribution of the Chi-Square Statistic

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

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

Type of Transportation and Commute Satisfaction

A survey of 530 commuters collected data on their primary mode of transportation (Car, Bus, Bike, Wa

Vehicle Type Distribution Goodness-of-Fit Test

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

Voter Initiative Support Homogeneity Test Across Regions

A study examines voter support for a new initiative in three regions: North, Central, and South. Ind

Voter Registration Distribution

A state expects voter registration to follow the proportions: Democratic 25%, Republican 35%, and In

Voting Methods: Chi-Square Goodness-of-Fit

In a local election, voters could choose from three voting methods: In-person, Mail-in, and Online.

Website Browser Market Share: Goodness-of-Fit Test

A tech website claims that the market share for internet browsers is as follows: Chrome 50%, Firefox

Advertising Data: Predicting Sales

A company wants to study how advertising spending (x, in thousands of dollars) affects product sales

Advertising Expenditure vs Sales

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

Advertising Spend and Website Traffic

A company analyzed how its weekly advertising spend (in thousands of dollars) influences website tra

Advertising Spending and Sales Revenue

A company collected data on its monthly advertising spending (in thousands of dollars) and correspon

Biomarker Levels and Disease Severity Simulation

A biomedical study examines the relationship between blood biomarker levels (in mg/dL) and disease s

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

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

Clinical Trial Dosage-Response Simulation

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

Consumer Spending and Income Levels

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

Daily Steps vs Calorie Burn

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

Effect of Study Intervention on Academic Performance

Researchers are evaluating whether participation in a new tutoring program predicts improvements in

Effectiveness of a New Drug on Blood Pressure

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

Employee Experience and Salary

A human resources study examines the relationship between years of work experience ($$x$$) and annua

Engineering: Stress and Strain in Alloys

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

Exercise Duration and Heart Rate Recovery

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

Fertilizer Effect on Plant Growth: Experimental Design

An agricultural study aims to assess the effect of different levels of fertilizer on plant growth. R

Hours of Training and Athletic Performance

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

Hours Practiced and Musical Performance Score

A music teacher is interested in whether the number of hours practiced per week is related to a stud

Internet Speed and Streaming Buffer Time

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

Manufacturing Quality Control: Regression Parameter Optimization Simulation

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

Marketing Strategy and Customer Visits

A retail chain implemented a new marketing strategy and analyzed its effect on the number of custome

Real Estate Regression Analysis

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

Relationship Between Temperature and Energy Consumption

A study of 30 households examined the relationship between the average outdoor temperature (in °F) d

Replicating Slope T-Test Using Summary Statistics

A researcher reports a sample slope of 2.5 with a standard error of 0.5 based on 12 observations. An

Retail Store Foot Traffic and Sales Revenue

A retail chain is studying the relationship between daily foot traffic (number of people) and daily

Social Media Advertising and Customer Clicks

A digital marketer investigates the relationship between social media advertising spending (x, in th

Social Media Use and Academic Performance

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

Software Development Efficiency: Lines of Code and Bug Count

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

Sports Performance: Training Hours and 100m Dash Times

For 20 professional athletes, a regression analysis was performed to predict 100m dash time (y, in s

Sports Training and Sprint Time

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

Stock Price and Market Index: Simulation of Slope Distribution

An economist is investigating the relationship between the daily returns of an individual stock and

Student Performance Analysis

A researcher investigates the relationship between the number of hours studied per week and improvem

Traffic Flow Analysis: Regression Slope Simulation

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