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

Analyzing Cumulative Frequency and Percentiles from Exam Scores

The cumulative frequency table below summarizes the scores on an exam for a class of 100 students:

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 $$

BMI and Blood Pressure Regression Analysis

A study examines the relationship between body mass index ($$BMI$$) and systolic blood pressure for

Categorical Data Analysis: Survey on Preferred School Year Length

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

Customer Satisfaction in Retail Chain

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

Customer Service Satisfaction by Service Type

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

Dotplot Representation of Home Run Distances

A dotplot displays the following frequencies for home run distances (in feet): • 387 appears once •

Error Rates in Two Production Machines

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

Event Attendance by Invitation Type

An event organizer tracked attendance based on invitation type (Digital, Paper) and the outcome (Att

Favorite School Lunch Choices

A survey was administered to 500 students about their favorite school lunch option. The partial data

Home Run Distance Analysis

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

Home Run Distances Analysis

Consider the following set of home run distances (in feet) measured at 13 ballparks: $$\{387, 400,

Investigative Task: Evaluating a School Breakfast Program

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

Marketing Campaign Reach by Region

A company tracked responses to a marketing campaign in two regions (Region 1 and Region 2) categoriz

Online Examination Scores

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

Parent Survey on School Length

A survey of 2000 parents asked which school year length they preferred. The following table summariz

Phone App Usage Times

Daily phone app usage is normally distributed with a mean of $$120$$ minutes and a standard deviatio

Regression Analysis: Blood Sugar and Calorie Intake

Researchers are studying the relationship between daily calorie intake and blood sugar levels measur

Shopping Satisfaction: Online vs. In-Store

A retail chain surveyed its customers to compare satisfaction between online shoppers and in-store s

Simulated Sampling Distribution of the Range from a Uniform Distribution

Consider a population with a uniform distribution on the interval [0, 1]. A simulation is performed

Simulation and Transformation Effects on the Sampling Distribution

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

Simulation of Taxi Annual Mileage Sampling Distribution

A researcher is investigating the annual mileage driven by taxi cabs in a metropolitan area. The pop

Social Media Platform Usage by Gender

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

Social Media Usage and Employee Productivity

A business is interested in evaluating whether limiting social media usage during work hours increas

Student Test Scores Improvement

A teacher implemented a new teaching method and collected exam scores from 35 students. The sample d

Treatment Outcomes in Hospital Study

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

Vehicle Type and Fuel Preference

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

Voting Behavior by Education Level

A political survey collected data on voters' education level (High School, College, Graduate) and th

Advertising Campaign and Sales Analysis

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

Analyzing Social Media Usage and Self-Esteem

A psychologist is studying the relationship between daily time spent on social media (x, in minutes)

Assessing Scatterplot Patterns: Nonlinear Relationships

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

Comparing Two Online Learning Platforms

An education technology firm wants to compare two online learning platforms to determine which one l

Customer Satisfaction Comparison at Two Store Branches

A retail company collected customer satisfaction data from two store branches, Branch A and Branch B

Customer Satisfaction: Online vs In-store Shopping

A retail company surveyed its customers about their satisfaction with online versus in-store shoppin

Employee Training Effectiveness

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

Environmental Study: Temperature and Ice Cream Sales

An environmental study tracked ice cream sales (in hundreds of dollars) and the daily high temperatu

Evaluating Coefficient of Determination in Athletic Performance

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

Evaluating Sales Team Performance

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

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

Forest Fire Risk Analysis

In a forested region, each of $$1000$$ acres has an independent probability of $$0.005$$ of burning

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

Impact of Caffeine Intake on Reaction Time

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

Least Squares Regression for Predicting House Prices

A real estate analyst collected data on several houses detailing their square footage (X) and corres

Predicting Fitness Improvement from Exercise Duration

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

Scatterplot Analysis: Teen Social Media Usage

A study collected data on the number of close friends (X) a group of teens reported and the number o

Simulation of the Sampling Distribution of a Cell Proportion in a Contingency Table

A study gathers categorical data in a two-way table regarding customer satisfaction (Satisfied/Not S

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

Transformation to Achieve Linearity: Population Growth

A rapidly growing town has recorded its population over a series of years, as shown in the table bel

Using Residual Plots to Assess Fit in Advertising and Sales Data

A company collects data on its weekly advertising budget (in $1000s, x) and weekly sales revenue (in

Website Click-Through Rate

An online advertisement has a click-through probability of $$0.15$$ for each visitor. Suppose that 5

Adverse Reaction Probability in a Drug Trial

In a clinical trial for a new drug, each patient has a 5% chance of an adverse reaction. In a sample

Analyzing Student Study Habits

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

Clinical Trial on Weight Loss Programs

A randomized controlled trial compares two weight loss programs. Program A (n = 40) results in an av

Cluster Sampling in Educational Testing

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

Commute Time and Job Satisfaction

A consulting firm conducts a study to examine whether longer commute times (in minutes, x) are assoc

Customer Feedback for a New Product

A technology company collected customer feedback regarding a new product via two purchasing channels

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

Ebola Outbreak Study

A retrospective observational study during an Ebola outbreak in West Africa collected data on the nu

Effect of Outliers on Sampling Distributions

In statistical analysis, outliers can notably influence the results of a study. Answer the following

Film Ratings Analysis

A movie review aggregator collects ratings on a scale from 1 to 10 from a simple random sample of 80

Firearm Safety Course Outcomes in Different Regions

A study examined the outcomes of a firearm safety course in two regions. In Region X, 160 out of 200

Impact of Advertising on Product Purchase

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

Impact of Advertising on Sales Revenue

A chain of retail stores seeks to understand the relationship between advertising expenditures (in $

Investigating Data Variability in Statewide Math Test Scores

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

Measurement Reliability in Climate Data Collection

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

Modeling Nonresponse in Simulation of Sampling Distributions

A survey is conducted to measure the average household electricity usage. In the simulation, a rando

Participation in Extracurricular Activities

A school examines its students' participation in extracurricular activities by grade level (Junior v

Salesperson Success: Geometric Probability

A salesperson meets potential customers, and the probability of making a sale during any meeting is

Sampling Variability in Teacher Performance Evaluations

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

Simulation of the Law of Large Numbers

A classic coin-flipping experiment is simulated to illustrate the Law of Large Numbers. In the simul

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

Smoking Impact on Lung Capacity: Regression Study

Researchers are investigating the relationship between the number of years a person has smoked (x) a

Systematic Sampling in a Voter Preference Survey

A polling organization is using systematic sampling to select registered voters from a telephone dir

Teaching Methods and Student Performance

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

Voting Preference Analysis

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

Website Traffic Sampling Distribution

A website typically records an average of 100 visitors per hour with a standard deviation of 15 visi

Binomial Distribution in Lightbulb Defectiveness

In a quality control test, the probability that a lightbulb is defective is $$0.1$$. Answer the foll

Coin Flip Game Strategies

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

Comparing Click-Through Rates of Two Advertising Campaigns

An online ad campaign was run using two different strategies. Campaign A achieved 210 clicks from 30

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

Customer Retention and Marketing Strategies

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

Daily Steps and Calorie Burn Regression Analysis

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

Defective Light Bulb Binomial Probabilities

Suppose the probability that a light bulb is defective is $$0.1$$. Consider independent selections o

Drug Efficacy in Clinical Trial

A pharmaceutical company claims that at least 70% of patients will show improvement after receiving

High School SAT Scores Analysis

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

Household Income and Entertainment Expenditure Regression Analysis

A survey of households examines the relationship between monthly income (in dollars) and monthly spe

Medical Screening Test Accuracy by Gender

A medical screening test was administered to 1000 individuals, 500 males and 500 females. The result

Scatterplot Regression Analysis on Study Habits

A researcher collects data on the number of hours students study (x) and their exam scores (y). The

Simulated Distribution of the Difference of Sample Means

In a simulation comparing two independent groups (for example, treatment and control), separate samp

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

Simulating Clinical Trial Successes

A new drug has a success probability of 0.65. In a clinical trial, 30 patients are treated independe

Small Business Daily Revenue Analysis

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

Social Media Post Engagement

A social media analyst is studying the engagement on posts from a popular brand. A random sample of

Student Testing Strategy and Scores Analysis

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

Suit Name Letter Count

A card is drawn from a standard 52-card deck. Let the random variable $$X$$ be the number of letters

Television Viewing Habits by Age and Time of Day

A survey of 300 television viewers recorded their preferred viewing times (Morning or Evening) acros

Urban Traffic Volume and Air Quality

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

Website Conversion Rates: A/B Testing

An online retailer is testing two different webpage designs. Landing Page A received 120 conversions

Website Navigation and Conversion Rates

A website conducted an A/B test with two versions (A and B) and recorded visitor conversion outcomes

Advanced Experimental Design in Teaching Methods

A researcher is investigating the effectiveness of two teaching methods by comparing student test sc

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

Caffeine Content in Energy Drink Boxes

A store sells boxes containing six bottles of an energy drink. The caffeine content per bottle is no

Coffee Bean Package Weight Analysis

A coffee company packages its coffee in bags. The weight of a coffee bag is normally distributed wit

Comparing Average Temperatures in Two Cities

City A has an average temperature of 70°F with a standard deviation of 5°F based on a sample of 50 d

Comparing Class Test Scores

Two independent classes took a standardized test. Class X (with $$n=30$$) had a mean score of 78 wit

Comparing Clinical Trial Drug Effects

In a clinical trial, two drugs are used to lower blood pressure. Drug A produces an average reductio

Comparing Variability: Averages versus Individual Values

In environmental testing, individual measurements of a pollutant level exhibit high variability. A s

Customer Complaints by Service Type

A telecommunications company recorded customer complaints for two types of services: Phone Service a

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

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

Election Polling Proportions

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

Employee Productivity by Shift

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

Hospital Patient Satisfaction by Department

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

Impact of Sample Size on the Standard Error

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

Lightbulb Life Expectancy Analysis

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

Naked Mole Rat Life Expectancy

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

New Drug Effect on Blood Pressure Reduction

A clinical trial is evaluating a new drug that is believed to reduce blood pressure. Historically, t

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

Polling Data Analysis

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

Public Health Study: Vaccination and Illness

In an effort to study the relationship between vaccination status and illness, public health officia

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 of a Sample Proportion for Disease

In a health study, it is known that 5% of the population has a particular disease. A random sample o

Sampling Distribution of Differences in Proportions

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

Simulated Daily Sales Distribution

A retail store simulated its daily sales over several months. The resulting sampling distribution of

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

Stock Returns Probability Calculation

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

Student Test Scores Sampling Distribution

An exam taken by a large group of high school students has scores that are approximately normally di

Advertising Impact on Brand Recognition

A company launched an advertising campaign in two regions. In Region 1, a post-campaign survey of 50

Analysis of Survey Data on Online Learning

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

Assessing Advertising Effectiveness with Proportion Data

An advertising firm claims that its new campaign results in a purchase rate of at least 30%. In an e

Business Model Customer Return Rate Comparison

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

Checking Inference Conditions for Proportion Data

A quality control study on a production process sampled 50 items and found that 47 met quality stand

Coffee Preference by Age Groups

A coffee shop surveyed customers on their coffee preference, classifying them as either preferring B

Computer Literacy Workshop Study

A community center is hosting two separate workshops aimed at improving computer literacy. At the en

Customer Satisfaction Survey

A company has collected customer satisfaction data from two sources. In-store customers (Group A) we

Determining Required Sample Size for Test Power

A public health researcher is testing the claim that the proportion of adults who smoke is less than

Employee Promotion Rates

A firm is comparing promotion rates between two departments. In Department A, 150 employees were sam

Evaluating Strike Support

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

Hospital Infection Rates: Hypothesis Testing

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

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

Interpreting a Confidence Interval for Hybrid Learning Preference

At a high school, a survey of 100 students reveals that 40 prefer a hybrid learning model.

Job Satisfaction by Shift Work

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

Marketing Strategies: Hypothesis Testing for Two Proportions

A company is comparing the response rates of two marketing campaigns. In Campaign A, 80 out of 250 c

Online Shopping Fraud Claims

An online survey compares the percentage of consumers who reported experiencing fraudulent transacti

Online Shopping Proportion Analysis

A market research firm surveyed 600 consumers to determine whether they prefer online shopping over

Political Opinion Poll Analysis

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

Research on Smoking Cessation Program

A study is conducted on a smoking cessation program to estimate the proportion of participants who s

Restaurant Hygiene Survey Analysis

A local health department collected data on restaurant hygiene. In a simple random sample of 100 res

Social Media Survey on Privacy Concerns

A survey conducted on a popular social media platform asked 800 users if they are highly concerned a

Student Housing and Meal Plan

A university surveyed students on their housing situation and meal plan status. Students are classif

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

Voter Initiatives on Environmental Policy

In a survey about a new environmental policy, 600 voters were asked whether they support the initiat

Voter Preference by Region

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

Analysis of Weekly Exercise Duration

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

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

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

Comparing 3-Point Percentage Rates

A sports analyst wants to compare the true 3-point shooting percentages of two basketball players. I

Comparing Two Diets

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

Comparing Two Methods of Estimating Reaction Time

A researcher is comparing two methods for measuring reaction time. Using Method 1 on a sample of 15

Customer Wait Time in Service

A supermarket manager records the wait times (in minutes) for customers at a checkout counter. In a

Daily Sales Confidence Interval

A store recorded its daily sales for 30 days, and the sample data yielded a mean of 200 units sold p

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

Drug Effectiveness on Blood Pressure

In a clinical trial, 35 patients are given a new drug and their blood pressures are measured before

Election Polling Power Analysis

In an election poll, a candidate claims to have 70% support. A critic believes the true support is 6

Employee Productivity Analysis

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

Employee Training and Productivity Outcome

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

Evaluating a Sleep Intervention

A fitness center implements a sleep intervention program aimed at increasing the average number of h

Fuel Efficiency of Hybrid Cars

A car manufacturer claims that its new hybrid model achieves an average fuel efficiency of at least

Gas Mileage Analysis: Confidence Interval Assessment

A manufacturer tests 12 cars of a new model. The sample yields a mean gas mileage of $$28.5$$ miles

Impact of a Study Program on Exam Performance

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

Machine Cycle Time Analysis

A manufacturing plant produces a critical component that goes through an automated production proces

Paired SAT Score Improvement

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

Physical Activity and Cholesterol Levels

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

Production Efficiency Comparison Across Shifts

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

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 Testing Under Caffeine Effects

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

Response Time in a Virtual Reality Task

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

Simulating the Effect of Sample Size on Confidence Interval Precision

A statistician performs a simulation study to examine the effect of sample size on the precision of

Simulation of Sampling Distribution for Mean Rainfall Amounts

A meteorologist simulates the sampling distribution of the average daily rainfall (in inches) record

Sodium Intake and Systolic Blood Pressure Analysis

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

Temperature and Ice Cream Sales Analysis

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

Test Score Improvement Analysis in a Preparation Class

In an SAT preparation class, 25 students took a pre-test and a post-test. The improvements (post-tes

Testing a New Drug's Effect on Cholesterol Levels

A pharmaceutical company claims that its new drug lowers LDL cholesterol levels. In a study of 12 pa

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

Training Program Performance Improvement

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

Academic Majors and Study Habits

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

Consumer Preference for Advertisement Types

A company believes that consumer preference for advertisement type follows the distribution: Online

Customer Feedback Comparison: Chi-Square Test in Service Industry

A service company collected customer feedback regarding satisfaction levels (Satisfied, Neutral, Uns

Customer Satisfaction Ratings Across Service Centers

Data has been collected from three service centers regarding customer satisfaction. The centers reco

Customer Satisfaction Survey Across Store Locations

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

Customer Service Feedback in Retail Stores: Homogeneity Test

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

DNA Mutation Distribution – Chi-Square Goodness-of-Fit

A geneticist hypothesizes that the distribution of DNA mutations in a sample of 300 cells is as foll

Drug Side Effects Analysis: Chi-Square Test for Independence

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

Effect of Marketing Campaign on Brand Awareness

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

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

Effectiveness of Advertisement Types

A study assesses whether the type of advertisement affects perceived effectiveness. Three ad types a

Extracurricular Participation and Academic Performance Independence Test

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

FRQ 4: Quality Control in Manufacturing Defects

A manufacturer claims that defects in its production process are distributed among three types: Type

FRQ 19: Comparing Library Usage Patterns Among Departments

A university library collected data on usage frequency categories (Frequent, Occasional, Rare) from

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

Game Outcome Distribution

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

Genotype Ratios: Goodness-of-Fit Test in a Biology Experiment

In a genetic cross, the expected Mendelian ratio for three genotypes is $$1:2:1$$. In a sample of 16

Goodness-of-Fit Test for Dice Fairness

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

Independence of Smoking and Lung Disease

A public health survey collected data from 300 participants to investigate the relationship between

Independence Test: Technology Adoption and Age Group

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

Major Distribution Across Colleges Goodness-of-Fit Test

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

Patient Outcomes by Treatment: Chi-Square Test for Independence

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

Phone Usage and Preferred App: Chi-Square Test for Independence

A tech survey collected data on 250 smartphone users on two categorical variables: phone operating s

Political Polling: Party Affiliation and Issue Stance

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

Preferred Study Methods: Homogeneity Test Across Colleges

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

Quality Control Across Production Lines – Chi-Square Test for Homogeneity

A company monitors the quality of items produced by three production lines. In monthly samples of 15

Restaurant Choices Across Regions: Chi-Square Test for Independence

A customer satisfaction survey collected data from 600 diners across three regions (urban, suburban,

Restaurant Menu Distribution Analysis

A popular restaurant chain claims that the distribution of orders among four cuisine types (Italian,

Social Media Platform Usage

A marketing agency expects that among 500 consumers, the usage of social media platforms is distribu

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

Annual Rainfall and Crop Yield

An agricultural researcher is examining the relationship between annual rainfall (x, in inches) and

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

Daily Steps vs Calorie Burn

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

Employee Experience and Salary

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

Employee Salary and Years of Experience

A human resources analyst uses years of experience (x) to predict annual salary in thousands of doll

Environmental Pollution and Distance Simulation

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

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

Ice Cream Sales vs Temperature

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

Interpreting Confidence Intervals from Multiple Studies

Two independent studies estimate the slope of a regression line that relates coffee consumption to p

Library Study Rooms Reservation vs Exam Success

A university service collected data on the number of library study room reservations made by student

Machine Runtime and Maintenance Costs

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

Manufacturing Process Optimization

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

Multiple Regression: Interpreting Slope in Presence of Collinearity

In a study using multiple regression to predict housing prices, several predictors (e.g., square foo

Online Engagement and Sales Conversion

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

Plant Growth and Fertilizer Amount

In an agricultural experiment, a researcher measured plant height (y, in cm) as a function of fertil

Predicting Sales Based on Advertising Budget

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

Residual Analysis in Housing Price Regression

A real estate analyst uses regression to model housing prices based on various features. A residual

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 (

Traffic Flow Analysis: Regression Slope Simulation

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

Traffic Volume and Pollution Levels

An environmental study was conducted over 45 days to assess the relationship between daily traffic v

Vehicle Weight and Fuel Efficiency

A study investigates the relationship between vehicle weight (in pounds) and fuel efficiency (in mil

Years of Experience and Salary Increase

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