AP Statistics FRQ Room

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:

Analyzing z-Scores from a Frequency Distribution

The following table displays z-scores along with their corresponding cumulative percentile rankings

AP Class Enrollment Analysis

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

Beverage Preference in Two Cities

A beverage company surveyed residents from two cities regarding their favorite drink. In City 1, 180

Calculating Variance and Standard Deviation for Book Counts

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

Charitable Donation Timing by Age Group

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

Comparative Analysis using Stem Plot and Histogram

Two groups of students took a standardized test. Group A's scores have a five-number summary: minimu

Comparing Sampling Distributions from Populations with Different Variances

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

Customer Ratings for Two Products

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

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 Price Increase on Customer Participation

A grocery store wanted to see if a recent price increase on a popular product affected customer part

Employee Salary Adjustments

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

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 Data Variability in Sports Statistics

A boxplot summarizes the points per game for a basketball player over a season with the following va

Home Run Distances Analysis

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

Hypothesis Testing: Reaction Time vs Age

In an experimental study on reaction times (in milliseconds) versus age (in years), the following re

Impact of Outliers on Measures of Center

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

Impact of Transformations on Data

Consider the following dataset representing test scores: {70, 80, 85, 90, 100}. Answer the followin

Interquartile Range and Boxplot Construction

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

Investigating Class Test Scores

A teacher collected the following test scores from a class: {55, 60, 62, 68, 70, 72, 75, 78, 80, 83,

Machine Adjustment Methods in Manufacturing

A manufacturing company wants to study the effect of two machine adjustment methods on production sp

NBA Wins: Analyzing Back-to-Back Stem Plots

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

Phone App Usage Times

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

Product Length Variability in Manufacturing

A manufacturing process produces items with lengths (in centimeters) distributed as shown in the fre

Sampling Distribution and Confidence Interval Implications for Household Incomes

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

Shopping Satisfaction: Online vs. In-Store

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

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 Campaign Effectiveness on Engagement

A company ran two social media campaigns to test engagement. In Campaign A, 250 out of 600 posts rec

Stock Price Trends Through Parallel Boxplots

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

Student Major and Internship Status

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

Study Program Effectiveness Hypothesis Test

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

Test Scores Histogram Interpretation

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

Unit Conversion Impact on Summary Statistics

A data set representing the lengths of objects is given in inches: {12, 24, 36, 48, 60}. Answer the

Analysis of Influential Points in Athlete Performance Data

A sports scientist investigates the relationship between training hours (x) and performance score (y

Analyzing Temperature Effects on Electricity Consumption

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

Attendance and Test Performance

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

City Bicycle Usage Study

A city bike‐share program collected data on daily high temperatures (in °F) and the total number of

Constructing a Contingency Table from Raw Data

A researcher surveying 100 individuals collected the following raw counts regarding gender (Male, Fe

Correlation vs. Causation Discussion

A study finds a high positive correlation between ice cream consumption and the number of drowning i

Daily Screen Time and Sleep Quality

A sleep study on 60 adults collected data on daily screen time (in hours, explanatory variable) and

Impact of a New Study App on Academic Performance

A technology company has developed a new study application intended to improve academic performance.

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

Online Ratings and Restaurant Revenue

A restaurant chain collected data on their average online rating (x, on a 5‐point scale) and corresp

Quality Control in Manufacturing

A factory produces light bulbs and historically 5% of bulbs are defective. A quality control inspect

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

Restaurant Service and Tipping

A restaurant manager collected data on the wait time (in minutes) experienced by customers and the c

Restaurant Tip Analysis

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

Simulating the Sampling Distribution of the Sample Mean in Bivariate Data

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

Simulation of the 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 Techniques and Exam Performance

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

Training Hours and Error Rates in Manufacturing

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

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

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

Analysis of Boxplots from an Experiment on Pulse Rates

Researchers conducted an experiment comparing the effects of three beverages (coffee, caffeinated co

Analysis of Smoking Habits Among Adults

A public health researcher surveyed adults and categorized them by age group (Young, Middle, Senior)

Analyzing Bias in Convenience Sampling at a Mall

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

Analyzing Sampling Variability Using Boxplots

A study on the ages of high school teachers uses four different sampling methods (A, B, C, and D) to

Assessing Nonresponse Bias in Telephone Surveys

During a telephone survey on community health, only 40% of the contacted individuals respond. Answer

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

Cluster Sampling in Educational Research

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

Comparative Simulation of the Mean and Median Sampling Distributions

A researcher simulates 1000 samples of size $$n = 30$$ from a moderately skewed population and calcu

Comparing Disease Incidence in Two Regions

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

Comparing Stratified and Cluster Sampling Methods in a Health Survey

A public health researcher is designing a survey to assess attitudes toward vaccination in a multi-n

Designing a Prospective Study for Teaching Methods

A school district wants to study the effect of a new teaching method on student performance on stand

Designing a Stratified Random Sample for Student Opinions on Distance Learning

A researcher intends to survey high school students' opinions on the transition to distance learning

Effect of Diet on Cholesterol Levels

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

Efficacy of a Mobile App for Tracking Physical Activity

A study compared the effectiveness of a mobile app in helping users meet their daily step goals. In

Environmental Pollution and Respiratory Health

Public health officials are studying the relationship between exposure to particulate matter (PM2.5,

Evaluating a Matched Pairs Design in a Weight Loss Study

Researchers compare two diets by having each participant follow both diets for a specified period, w

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

Heart Rate Recovery and Fitness Level

In a cardiovascular fitness study, researchers examine if higher fitness levels (measured by a fitne

Monte Carlo Simulation and the CLT

A researcher conducts a Monte Carlo simulation by drawing 1,000 random samples, each of size 30, fro

Online Tutoring and Student Performance

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

Public Health Intervention on Smoking Cessation

A city public health department wants to evaluate the effectiveness of a new anti-smoking campaign i

Retrospective Study on Environmental Exposure and Health Outcomes

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

Screen Time and Anxiety Levels

A psychologist studies the relationship between daily screen time (in hours, x) and self-reported an

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

Social Media Usage among Teenagers

A survey of teenagers collected data on social media platform preferences (Instagram, Snapchat, TikT

Social Media Use and Academic Performance

A study is conducted to explore the relationship between daily hours spent on social media (x) and a

Urban Green Spaces and Air Quality

An urban planning study is being conducted to determine whether proximity to green spaces is associa

Apartment Rental Prices Estimation

A real estate researcher is studying monthly apartment rents in a metropolitan area. In a random sam

Basic Probability Rules in Testing Strategies

A standardized test uses different strategies when a student is uncertain about an answer. The table

Binomial Process in Quality Testing

A quality control inspector tests a batch of 100 light bulbs. Each bulb has a 10% chance of being de

Campus Computer Virus Spread: Multistage Probability Calculation

On a university campus, computers run on three different operating systems: Windows (60%), Apple (30

City Traffic Speed Analysis

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

Comparing Bank Loan Approval Rates

A bank uses two different underwriting policies. Under Policy A, 300 out of 500 applicants are appro

Comparing Customer Satisfaction in Two Coffee Shops

A survey was conducted to compare customer satisfaction between two coffee shops. The table below su

Comparing Daily Step Counts: Traditional Pedometer vs Fitness Tracker

A study compared the daily step counts of two groups: one group used a traditional pedometer (n = 50

Comparison of Incident Rates between Day and Night Shifts

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

Energy Consumption Random Variables

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

Evaluating a Mobile App to Promote Healthy Eating

A public health researcher is testing a mobile app designed to promote healthy eating habits. Volunt

Event Planning and Rainy Days: Binomial Analysis

An event planner considers a month of 30 days where the probability of a rainy day is $$0.3$$, indep

Exam Score Cumulative Distribution

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

Exercise Time and Cholesterol Level Regression Analysis

A health study examining the effect of weekly exercise on cholesterol levels among 80 adults produce

First Honest Encounter: Geometric Distribution

In ancient Greece, suppose only 12% of men are honest. Let \(X\) represent the trial on which the fi

Fuel Efficiency Comparison between Two Vehicle Models

An automotive study compared the fuel efficiency of two car models. Model X was tested on 30 cars, y

Geometric Distribution: Encountering an Honest Person

Imagine that the probability a randomly encountered man in ancient Greece is honest is $$0.12$$. Let

Impact of Meditation on Stress Reduction

A mental health clinic is studying whether an 8‐week meditation program reduces stress levels in its

Impact of Sleep Duration on Reaction Time

A research lab is investigating how different amounts of sleep affect reaction times measured on a s

Impact of Social Media Usage on Academic Performance

A study is conducted to examine the relationship between time spent on social media and academic per

Medical Screening Test Accuracy by Gender

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

Monthly Supermarket Expenditures

A local supermarket chain wants to estimate the average monthly expenditure of its customers. A rand

Online Shopping Behavior by Time of Visit

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

Quality Control in Manufacturing

A factory produces items with a defect probability of $$0.05$$ per item. Items are produced in batch

Retail Customer Purchases: Random Variable Analysis

A survey at a retail store reveals that the number of items purchased per visit follows this distrib

Scatterplot Regression Analysis on Advertising and Sales

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

Simulated Sampling Distribution of the Sample Variance

A simulation is conducted by drawing samples from a normal distribution with $$\mu = 20$$ and $$\sig

Startup Daily Profit Analysis

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

Suit Name Letter Count

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

Tip Amounts from Different Meal Services

At a restaurant, a waiter receives tips from two independent services. For lunch, the tip is modeled

Transforming Game Winnings

A game offers winnings with the following outcomes: | Winnings ($$\$\$$) | Probability | |---------

Transforming Payouts in a Carnival Game

A carnival game pays out according to a random variable $$X$$ with outcomes: $10 (p = 0.4), $20 (p =

Weather Temperature and Ice Cream Sales Regression Analysis

A vendor investigates the relationship between daily temperature (in °F) and ice cream sales (in dol

Analyzing Daily Coffee Sales Sampling Distribution

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

Biased Estimator in Manufacturing

In a factory, two different devices (Device X and Device Y) are used to measure the length of metal

Central Limit Theorem in Transportation: Bus Arrival Times

The delays in bus arrivals in a city are skewed with a mean delay of 8 minutes and a standard deviat

Comparing Customer Satisfaction Among Two Stores

A retail chain conducts a study comparing customer satisfaction levels. In store A, 85% of customers

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 Variability: Averages versus Individual Values

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

Consumer Reviews: Variability Analysis

A popular online product has consumer ratings on a 1-to-5 star scale. In a random sample of 100 revi

Difference in Proportions: Fast Food Restaurant Study

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

Dream Recall Simulation Study

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

Effect of Outliers on Sampling Distribution of the Mean

A dataset on household incomes is highly skewed due to extreme values. A statistician takes random s

Effect of Sample Size on Variability

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

Election Polling Proportions

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

Evaluating Math Anxiety and Brain Activity

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

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

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

Impact of Sample Size on the Standard Error

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

Normal Distribution Calculation: Component Lifespan

A certain machine component has a lifespan that is approximately normally distributed with mean $$\m

Political Opinion Poll on Policy Support

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

Public Health Study: Vaccination and Illness

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

Simulation Study of Income Medians

A researcher studies household incomes, which are heavily right-skewed. The population has a median

Student Test Scores Sampling Distribution

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

Analyzing Election Poll Data: Estimating the Margin of Error

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

Analyzing Voter Turnout Using Confidence Intervals

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

Comparative Analysis of Two Healthcare Clinics

Two healthcare clinics are comparing the success rate of a new treatment. At Clinic 1, 80 out of 100

Comparing Participation Rates in Exercise Programs Across Cities

Two cities conducted surveys about participation in exercise programs. City X had 250 participants o

Comparing Two Dietary Supplements

A study compares two dietary supplements. In a sample of 200 consumers for Supplement A, 140 reporte

Confidence Interval for Social Media Users

A survey was conducted on 800 individuals to assess daily social media usage. Out of 800 respondents

Customer Loyalty Program Impact Study

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

Customer Satisfaction Survey by Region

A retail company conducted a customer satisfaction survey in two regions, North and South. Responses

Designing a Survey for Voting Behavior

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

Effect of an Advertisement on Purchase Intent

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

Employee Promotion Rates

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

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

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

Online Shopping Behavior

A survey of customers on an e-commerce website evaluated purchasing behavior across two age groups:

Online Shopping Fraud Claims

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

Opinion Poll on Environmental Policy

A survey of 600 citizens was conducted to gauge support for a new environmental policy. Out of the 6

Reading Program Impact Study

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

Retail Coupon Usage Among Customers

Two retail outlets want to know if they differ in the rate of coupon usage among their customers. Ou

Sample Size Determination for Desired Margin of Error

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

School Intervention Study

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

Sports Participation by Gender and Sport Type

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

Sports Statistics: Free Throw Confidence Interval

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

University Enrollment Statistics

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

Voting by Race

A political science study collected data on voting behavior by race. Voters are classified as either

Blood Pressure Reduction Confidence Interval

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

Coffee Shop Wait Times

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

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 Manufacturing Processes

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

Comparing New Drug Efficacy

A pharmaceutical study compares two medications for lowering blood pressure. Group 1 (Drug A) consis

Comparison of Pollutant Concentration in Two Rivers

Environmental scientists measured the pollutant concentration (in mg/L) in two rivers. River 1 was s

Comparison of Waiting Times: Urban vs. Rural Hospitals

A health researcher compares patient waiting times in emergency rooms between urban and rural hospit

Detection of Production Process Anomalies via Simulation

A factory monitors its production process by measuring the deviation from a target product dimension

Dosage Effect on Symptom Reduction

In a clinical trial investigating the effect of a drug, researchers examine the relationship between

Effectiveness of Drug Treatments

A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients

Enzyme Activity Confidence Interval

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

Evaluating a Mobile App's Impact on Daily Step Count

A health technology firm develops a new mobile application aimed at increasing daily physical activi

Exercise and Resting Heart Rate Analysis

The scatterplot below shows data from a study on the relationship between weekly exercise hours (x-a

Fertilizer Impact on Plant Growth

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

Fuel Efficiency of Hybrid Cars

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

Machine Cycle Time Analysis

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

Monthly Sales Performance Analysis

A retail store assesses the impact of a promotional campaign on monthly sales. The data collected co

Pre- and Post-Treatment Blood Pressure

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

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 Sampling Distribution of Daily Temperatures

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

Simulation of Sampling Distribution for Average Calorie Content in Energy Bars

A food quality control manager conducts a simulation study to evaluate the average calorie content o

Simulation of Sampling Distribution for Mean Recovery Time

A hospital administrator runs a simulation study to assess the average recovery time (in days) after

Simulation of Sampling Distribution in Environmental Air Quality

An environmental scientist conducts a simulation study to analyze the sampling distribution of the 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

Study on Sleep Duration Effects

A research study investigates whether sleep duration affects employee productivity. In a random samp

Test Score Comparison between Two Classes

Two different classes took a standardized test. Class A (n = 30) had a mean score of 78 with a stand

Weight Loss Study Confidence Interval

A nutritionist is studying the effect of a new diet on weight loss. A random sample of 16 subjects y

Age Group and Exercise Habits

A fitness survey categorizes participants into three age groups (Teen, Adult, Senior) and records th

Analyzing Website Navigation: Chi-Square Test for Independence

A study examining whether the navigation path taken on a website is related to the type of device us

Association between Exercise Frequency and Diet Type

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

Candy Flavor Preferences: Goodness-of-Fit Test

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

Car Color and Accident Involvement: Independence Test

An insurance company collects data on car color and accident involvement among 500 policyholders. Th

College Major and Part-Time Job: Independence Test

A study examines the association between college major and part-time job status. The data collected

Consumer Brand Preference Homogeneity Test

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

Customer Product Color Preference Analysis

A company conducts a survey on customer preferences regarding the color of a new product. The compan

Distribution of Housing Types in a City

A city planning department is examining the distribution of housing types in the city. They expect t

Effect of Marketing Campaign on Brand Awareness

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

Employee Job Satisfaction by Department: Chi-Square Test for Homogeneity

A company surveys employees from three different departments (Sales, Engineering, HR) about job sati

Employee Training Program: Comparing Certifications Across Departments

A company is evaluating the effectiveness of a new training program by comparing certification rates

FRQ 1: Distribution of Customer Preference for a New Snack

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

FRQ 2: Association Between Smoking Behavior and Gender

A public health survey collected data on smoking status and gender from 150 individuals. The observe

FRQ 6: Association Between Diet and Heart Disease Risk

A study investigates whether there is an association between diet type and heart disease risk. The s

FRQ 7: Comparing Satisfaction Levels Across Service Centers

A company wants to determine if customer satisfaction is consistent across three service center bran

FRQ 15: Distribution of Wildlife Species in a National Park

Park managers expect that wildlife sightings in a national park follow a certain distribution among

Homogeneity in Student Class Preferences

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

Independence Test: Health Food Consumption vs. Age Group

A study collected data on whether individuals regularly consume organic foods (Yes/No) across three

Independence Test: Voting Preference and Gender

A survey of 500 voters collected data on voting preference (Candidate A, Candidate B, Other) and gen

Insurance Claim Types: Independence Test Across Age Groups

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

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

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

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

Participation in Extracurricular Activities: Chi-Square Test for Homogeneity

A school district wants to compare participation rates in extracurricular activities among high scho

Product Packaging Preference Across Regions

A company wants to verify if the color preference for product packaging is consistent across three d

Satisfaction Survey Among Product Users: Chi-Square Test for Independence

A company wants to investigate whether customer satisfaction is independent of product type. A surve

Simulated Chi-Square Distribution for Voting Patterns

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

Simulating the Distribution of the Chi-Square Statistic

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

Species Distribution in a Wildlife Reserve

In a wildlife reserve, the theoretical model predicts that the species distribution should be: Mamma

Transportation Mode Among City Residents

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

Transportation Mode Preferences: Homogeneity Test in City vs. Suburban Areas

An urban planner surveyed residents in a city and a suburban area about their preferred transportati

Vehicle Type Distribution Goodness-of-Fit Test

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

Voter Preferences Among Four Candidates – Chi-Square Goodness-of-Fit

An election poll of 800 voters reports the following counts for four candidates: Candidate A: 220, C

Wildlife Habitat Preference: Chi-Square Goodness-of-Fit

Ecologists are studying the distribution of a particular species among four habitat types: Forest, G

Advertising Budget and Sales Revenue

A marketing analyst is studying the relationship between a company’s monthly advertising budget (in

Advertising Impact on Sales

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

Air Quality and Traffic Flow

A study investigates whether daily traffic flow (vehicles per hour) is associated with urban air pol

Assessing Environmental Pollution Impact

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

Biking Speed and Heart Rate

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

Car Fuel Efficiency and Engine Size Comparison

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

City Population and Public Transportation Usage

A city planner is investigating whether there is a linear relationship between city population (in t

Clinical Trial Dosage-Response Simulation

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

Environmental Pollution and Distance Simulation

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

Exercise and Cholesterol Reduction

A health study investigated the effect of weekly exercise hours (x) on cholesterol reduction (y, in

Exercise Duration and Heart Rate Recovery

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

Internet Speed vs. Streaming Delay

A study of 30 households examines the relationship between internet speed (in Mbps) and video stream

Manufacturing Process Optimization

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

Marketing Campaign Effectiveness Simulation

A marketing analyst is examining the relationship between advertising spending (in dollars) and sale

Marketing Impact: Social Media Activity vs. Product Sales

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

Measurement Error Impact on Slope Estimation: Simulation Study

An industrial engineer investigates the relationship between machine speed (in rpm) and the number o

Medication Dosage and Recovery Time

A clinical trial explores the impact of a new drug's dosage (measured in mg) on recovery time (measu

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 Course Participation and Final Grade

An education researcher is analyzing whether the number of online course modules completed by studen

Physical Activity and Weight Loss: Simulation Analysis

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

Predicting Ice Cream Sales from Temperature

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

Rainfall and Crop Yield

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

Residual Analysis in Housing Price Regression

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

River Pollution Levels and Industrial Activity

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

Robotics and Efficiency

A robotics company collects data from 15 production lines to examine the relationship between the nu

Social Media Advertising and Customer Clicks

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

Sports Training and Sprint Time

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

Temperature Effect on Ice Cream Sales

An ice cream vendor recorded daily temperature (in °F) and daily ice cream sales (in dollars) over 3

Traffic Volume and Pollution Levels

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

Urban vs Rural Pollution Levels

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