AP Statistics FRQ Room

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}.

Community Exercise Program and Blood Pressure Reduction

A public health study is conducted to evaluate the effectiveness of a community exercise program on

Comparing Sleep Hours in High School and College Students

Two histograms display the number of hours of sleep per night for high school and college students.

Customer Satisfaction in Retail Chain

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

Customer Satisfaction in Two Regions

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

Daily Caloric Intake Data Analysis

A nutrition study collected data on the daily caloric intake of 170 individuals. The results, broken

Digital Flashcards vs. Traditional Study for Vocabulary Improvement

A study is conducted to compare the effectiveness of a digital flashcards app versus traditional pap

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

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

Effectiveness of a New Wearable Heart Rate Monitor

A tech company is evaluating whether a new wearable device provides more accurate measurements of he

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

Event Attendance by Invitation Type

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

Exam Scores: Descriptive Statistics

A teacher collected the scores from a recent exam. The data are summarized in the frequency table be

Home Run Distances in Ballparks

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

Measures of Variability in Teacher Ages

The ages of 12 mathematics teachers at a high school are: {24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 5

Nature Exposure and Mood Improvement

An environmental psychology study is designed to assess whether guided nature walks improve mood amo

Nutrition Study: Effects of Diet on Weight Loss

A nutritionist intends to study whether different diets lead to different average weight losses over

Political Affiliation and Media Consumption

A study surveyed 300 voters on their political affiliation (Party A, Party B, Independent) and their

Restaurant Wait Time Analysis

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

Simulated Sampling Distribution of the Standard Deviation

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

Simulation and Transformation Effects on the Sampling Distribution

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

Simulation of the Sampling Distribution for the Sample Variance

Consider a normally distributed variable with a true variance of $$\sigma^2 = 16$$. A researcher sim

Social Media Platform Usage by Gender

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

Sports Participation and Club Membership

A college survey collected data on students' participation in sports (Yes, No) and their club member

Stemplot Construction: Analyzing a Data Set

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

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

Analyzing Temperature vs. Ice Cream Sales

An ice cream shop collected data over a summer month to assess the relationship between daily temper

Assessment of Internet Usage and Academic Performance

A study examines the relationship between the number of hours college students spend online per day

Coffee Shop Drink Preference

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

Coffee Shop Sales Analysis

A local coffee shop has recorded data on daily advertising expenditure (in dollars) and the correspo

Comparing Marginal and Conditional Distributions in a Two-Way Table

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

Consumer Product Satisfaction

A market research study evaluates consumer satisfaction with two new smartphone models. After using

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.

Customer Satisfaction and Purchase Frequency

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

Customer Satisfaction Comparison at Two Store Branches

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

Dietary Effects on Blood Pressure

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

E-Commerce Site Traffic and Revenue Analysis

An e-commerce website collected data on daily visitor counts (x) and corresponding sales revenue in

Effectiveness of a Medical Treatment

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

Effects of Dropping a High-Leverage Observation

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

Employment Rates of College Graduates

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

Forest Fire Risk Analysis

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

Green Energy Adoption and Energy Savings

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

Highway Traffic Flow and Accident Rates

A study examined 25 highways to investigate the relationship between average daily traffic flow (x,

Impact of Sleep on Mental Health Scores

A psychologist investigates the relationship between the average number of hours of sleep per night

Local Policy Impact: Public Transportation and Commute Times

A city council is evaluating the effectiveness of recent public transit improvements. They collected

Manufacturing Defects in Two Production Lines

A manufacturing company operates two production lines. A quality control inspection was performed on

Public Health Campaign on Smoking Cessation

A public health department launched a campaign to help individuals quit smoking. A study was conduct

Quality Control in a Bakery

A bakery finds that historically 2% of its cookies are too hard. In a sample of $$100$$ cookies, let

Regression Analysis of Movie Attendance and Concession Sales

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

Sampling Distribution of the Coefficient of Determination (\(r^2\)) via Simulation

Researchers study the relationship between study time and exam scores and want to understand the sam

Sampling Distribution of the Sample Range and Its Limitations via Simulation

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

Specialty Coffee Orders at a Coffee Shop

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

Study Habits and Exam Scores: Regression Inference

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

Temperature and Ice Cream Sales

An ice cream vendor records daily maximum temperatures (in degrees Fahrenheit) and the number of box

Urban Noise and Sleep Quality Study

A study investigated the impact of urban noise level (measured in decibels, x) on individuals' self‐

Voter Approval Polling

Preliminary polls indicate that 45% of voters approve of a candidate. A random sample of $$200$$ vot

Analyzing Sampling Variability with Box Plots

A study is conducted to estimate the average test score for teachers in a school district. Four diff

Assessing Sampling Techniques in Market Research for a New Product

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

Assessing Systematic Sampling in a Household Survey

A market research firm wants to survey household expenditures and decides to use systematic sampling

Bias in Random Digit Sampling

A researcher uses random digit dialing to contact households for a survey. However, certain demograp

Coffee Consumption and Productivity: Observational Study

A tech company conducted an observational study on the relationship between the number of cups of co

Comparing Test Scores Between Two Teaching Methods

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

Comparing Treatment Efficacy in a Retrospective Study

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

Customer Loyalty Programs: New vs. Established Store

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

Data Collection in a Prospective Observational Study

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

Designing a Prospective Study for a Drug Trial

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

Diet, Weight Loss, and Regression Analysis

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

Evaluating Bias in Voluntary Response Surveys

A local government agency conducts a survey on community satisfaction with public transportation thr

Evaluating Survey Question Wording Bias

Two versions of a survey question on school lunch satisfaction have been designed. Version A states:

Internet Usage and Education Level

A study analyzed internet usage frequency (Daily, Weekly, Rarely) among individuals with different e

Interpreting a Scatterplot from a Survey on Sleep and Test Scores

A study surveys high school students regarding their average nightly sleep (in hours) and their most

Investigating Voluntary Response Survey Bias

A mid-sized university is conducting an online survey about campus safety. The survey is distributed

Matched Pairs Design in a Dietary Study

A nutritionist wants to compare the effectiveness of two diets on weight loss. To control for initia

Placebo-Controlled Experiment in Nutritional Supplements

Researchers are studying the effect of a new nutritional supplement on muscle recovery times. Partic

Predicting Blood Pressure from Age: Regression and Inference

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Simulating Sampling Distributions for Quality Control in Manufacturing

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

Simulating the Sampling Distribution from a Skewed Distribution

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

Simulating the Sampling Distribution of Exam Scores

A teacher is interested in understanding the variability of exam scores in her class. The population

Simulation Study on the Distribution of the Sample Range

A researcher is studying the spread of values in a uniformly distributed population on the interval

Smartphone Usage and Sleep Quality

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

Traffic Flow System and Commuting Times

A city is testing a new traffic flow system designed to reduce commuting times during rush hour. The

Ad Spend and Market Share Regression Analysis

A market analyst investigates the relationship between advertising spend (in millions of dollars) an

Basketball Free Throw Analysis: Binomial and Transformation

A basketball player has a free throw success rate of $$0.75$$ and takes $$16$$ free throws in a game

Campus Computer Virus Spread: Multistage Probability Calculation

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

Car Purchase Decisions by Region

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

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 Click-Through Rates of Two Advertising Campaigns

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

Evaluating a New Teaching Technique in High School

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

Fitness Center Membership Duration

A fitness center wishes to estimate how long its members typically stay subscribed. A random sample

Highway Worker Productivity

A construction team has three possible outcomes for the number of miles of highway built in a day: 4

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 Study Aid on Exam Pass Rates

A school collected data on standardized exam pass rates. Among students who used a study aid, 85 out

Lottery Ticket Expected Outcome

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

Manufacturing Process Downtime

A factory records daily machine downtime (in hours) due to equipment failures according to the follo

Medical Trial for a New Drug

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

Online Retail Shipping Time

An online retailer wants to evaluate its shipping performance. In a sample of 30 shipments, the mean

Simulated Binomial Sampling Distribution

A simulation experiment involves performing 20 independent Bernoulli trials with a probability of su

Simulated Sampling Distribution of Survey Proportions

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

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

Traffic Accident Analysis

A city records the number of traffic accidents per day over a month. The observed distribution is gi

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 =

Transportation Delay Times

A city's bus service experiences delays (in minutes) according to the following distribution: | Del

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

Constructing a 95% Confidence Interval for Battery Lifetime

A quality control study tests the lifetimes of batteries. A random sample of 50 batteries has a samp

Customer Complaints by Service Type

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

Differences in Genetic Mutations by Age

A study investigates the number of genetic mutations contributed by fathers of different ages. For 4

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

Emergency Room Wait Times Analysis

In a hospital, emergency room wait times are approximately normally distributed with a mean of 30 mi

Evaluating Manufacturing Estimators

A factory produces widgets with a true length of 150 mm. Five different estimators (A, B, C, D, and

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 Devices on Online Purchases

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

LED Lightbulb Lifespan Probability Analysis

A manufacturer produces LED lightbulbs whose lifespans are normally distributed with a mean of $$\mu

Political Opinion Poll on Policy Support

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

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

Simulation Study of Income Medians

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

Survey on Learning App Preference

In a high school, it is believed that $$65\%$$ of students prefer using a new learning app. A random

Survey on Policy Support in Two Regions

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

Survey on Preferred Beverage

A beverage company surveys 150 customers to estimate the proportion who prefer its new soda flavor.

Training Techniques and Marathon Finish Times

A sports scientist is comparing the effectiveness of two training methods on marathon finish times.

Unbiased Estimators: Evaluating Sample Slope

In a study of the relationship between hours studied and exam scores, a simple linear regression is

Voting Behavior by Gender

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

Analysis of Survey Data on Online Learning

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

Assessing New Advertising Campaign Effectiveness

A company runs a new advertising campaign. Out of 400 customers, 160 made a purchase within 24 hours

Assessing Website Conversion Rate

A company claims that its website has a conversion rate of 5%. To test this claim, a random sample o

Community Recycling Program Study

A city implements a program aimed at increasing household recycling rates. Two neighborhoods with si

Comparing Satisfaction Between Two Stores

A retail chain wants to compare customer satisfaction between two of its stores. In Store A, 150 cus

Comparing Two Methods for Quality Control in Manufacturing

A manufacturing company compares two quality control methods. In a trial run, Method A identified 95

Confidence Interval for Proportion in Market Research

A market research firm surveys 500 consumers and finds that 265 like a new product.

Drug Effectiveness Hypothesis Test

A pharmaceutical company claims that its new drug is effective in 80% of patients. To test this clai

Effect of an Advertisement on Purchase Intent

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

Environmental Study: Testing Proportion Exceeding Safety Threshold

A study of water quality in a river found that 18 out of 90 samples exceeded the safety threshold fo

Government Policy Approval Confidence Interval

A polling organization surveyed 800 voters to measure the approval of a recent government policy. Am

Measuring Customer Preferences

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

Medical Trial: Comparing Treatment and Control

A clinical trial compares the effectiveness of a new treatment with a placebo. In the treatment grou

Political Polling: Estimating Voter Support

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

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 quality control study in manufacturing compares two plants. In Plant 1, out of 500 items produced,

Research on Smoking Cessation Program

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

Retail Coupon Usage Among Customers

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

Smartphone Brand Preference by Income Level

A market research survey categorized respondents by income level and their preferred smartphone bran

Social Media Influence Study

A marketing firm is investigating whether exposure to a popular social media influencer affects the

Sports Participation by Gender and Sport Type

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

Student Housing and Meal Plan

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

Testing for a Rare Event Proportion

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

Traffic Accident Analysis

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

Urban vs Rural Voter Support Analysis

A political poll collected data from two independent groups: urban voters and rural voters. In the u

Urban vs. Rural: Survey on Public Transportation Usage

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

Vaccine Hesitancy Survey Design

Public health officials are conducting a survey to estimate the proportion of individuals who are he

Voter Preferences by Age Group

A recent survey collected data on voter preferences for two political candidates among voters in two

Accident Frequency Comparison

An assembly plant records the number of accidents per month in two independent departments over 30 m

Battery Life Study

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

Blood Pressure and Sodium Intake Regression

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

Change in Manufacturing Process: Product Lifespan

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

Coffee Consumption and Alertness Scores

A study investigates whether coffee consumption affects alertness. Two independent samples are consi

Comparing 3-Point Percentage Rates

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

Comparing Average Heart Rates in Two Exercise Regimens

A fitness study compared the effects of two different exercise regimens on heart rate. Group 1 (n =

Comparing Delivery Times

A logistics company is comparing two shipping methods to determine which is faster. For method A, a

Comparing Recovery Times in Two Hospitals

A study compares patient recovery times (in days) following a standard surgical procedure at two dif

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

Comparing Two Treatments for Improvement

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

Comparison of Pollutant Concentration in Two Rivers

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

Customer Preference on Smartphone Features

A market research survey evaluates customer satisfaction for two smartphone brands, Brand A and Bran

Daily Steps: Wearable Device Analysis

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

Determining Sample Size for a Cholesterol Study

A researcher aims to estimate the mean cholesterol level in a population with a margin of error of 2

Dosage Effect on Symptom Reduction

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

Drug Effectiveness on Blood Pressure

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

Effectiveness of Tutoring Program Investigation

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

Energy Consumption Analysis

An energy company is testing the claim that the average daily electricity consumption of households

Exam Score Analysis with Unequal Sample Sizes

A researcher compares exam scores between two sections of a course. Section A (n = 18) has a mean sc

Impact of a Study Program on Exam Performance

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

Income Analysis for a Tech Company

A tech company wants to estimate the average annual bonus received by its employees. A survey of 22

Mean Gas Mileage Confidence Interval

A car manufacturer wants to estimate the true mean gas mileage of a new model. A random sample of 12

Medical Device Response Time Analysis

A study is carried out to evaluate the response time (in seconds) of a new medical device. A random

Project Completion Times

A company is evaluating the effect of a process improvement by comparing project completion times be

Quality Control Analysis using Simulation-Based P-Value

In a manufacturing process, quality control involves monitoring the variability of a key dimension u

Quality Control in Production

A company tests the tensile strength of its products. A random sample of 12 items shows a sample mea

Rainfall Measurement Study

A meteorologist records daily rainfall (in mm) over 20 days in a region. The sample has a mean of 12

Simulating Sampling Distribution of Chip Weight

A chip manufacturing factory is investigating the average weight of its chips. A simulation was perf

Simulation of the Sampling Distribution for Mean Internet Connection Speeds

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

Simulation of the Sampling Distribution for Mean Salary

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

Soil pH Variation

An agricultural experiment is conducted to assess whether a new fertilizer treatment helps bring soi

Temperature and Water Consumption Analysis

The scatterplot below shows data on daily temperature in °F (x-axis) and water consumption in gallon

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 Mean Daily Water Consumption

A municipal claim states that the mean daily water consumption in a city is 150 liters. A survey of

Training Program Performance Improvement

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

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

Advertising Channels Effectiveness: Homogeneity Test

A company wants to determine if the effectiveness of three advertising channels (TV, Online, Print)

Assessing the Fit of a Theoretical Distribution on Emergency Call Durations

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

Brand Preference Across Age Groups – Chi-Square Test for Homogeneity

A survey was conducted to determine the preferred soft drink brand (Brand X, Brand Y, Brand Z) among

Comparing Preferences for Social Media Platforms Across Age Groups

A survey examines if social media platform preference is associated with age group. The data collect

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

Customer Satisfaction Across Store Branches: Chi-Square Test for Homogeneity

A retail chain surveys customer satisfaction across three store branches. Customers are classified a

Drug Efficacy Across Dosages

In a clinical trial, patients were randomly assigned to receive one of three dosages (Low, Medium, H

Evaluating Marketing Strategies: Chi-Square Test for Independence with a Simulation Component

A marketing firm wants to determine if there is an association between consumer purchase behavior (B

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 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 12: Employee Training Program and Job Promotion

A company is investigating the effectiveness of its training program on job promotions. The collecte

FRQ 13: Customer Loyalty Across Store Branches

A chain store wants to investigate whether customer loyalty is consistent across its four branches.

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

Gender and Preferred Social Media Platform

A survey of 300 teenagers gathered data on their gender (Male, Female) and their preferred social me

Goodness-of-Fit for Beverage Preferences

A local cafe expects customer beverage preferences to follow the distribution: Iced Coffee (40%), Ho

Goodness-of-Fit in Genetic Ratio for Pea Plants

In a genetics experiment, pea plants are expected to exhibit a 3:1 ratio for purple to white flowers

Goodness-of-Fit Test for Web Traffic Sources

A website manager expects that web traffic comes from four sources with the following proportions: D

Homogeneity in Customer Service Satisfaction Across Branches

A retail chain wants to determine if customer satisfaction (Satisfied, Neutral, Unsatisfied) is homo

Homogeneity in Voter Turnout Among Demographic Groups

Exit polls in three different cities recorded voter turnout (Voted, Did Not Vote). Use the data to t

Independence Test: Voting Preference and Gender

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

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

Simulating the Distribution of the Chi-Square Statistic

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

Smoking and Exercise Frequency Independence Test

A health survey categorizes individuals by smoking status (Smoker, Non-Smoker) and exercise frequenc

Social Media Platform Usage

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

Socioeconomic Status and Book Reading Frequency: Independence Test

A survey of 600 individuals collects data on their socioeconomic status (Low, Medium, High) and book

Subscription Plans and Customer Region – Chi-Square Test for Independence

A streaming service collects data on customer region (North, South, East, West) and their chosen sub

Survey of Smartphone OS Usage

A national survey collected data from 400 respondents on their smartphone operating system preferenc

Teacher Satisfaction by Department: Chi-Square Test for Homogeneity

A school district wishes to determine if job satisfaction among teachers varies by department (Math,

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

Voting Methods: Chi-Square Goodness-of-Fit

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

Advertising and Sales Revenue Regression Analysis

A marketing firm is studying the relationship between advertising spending (in thousands of dollars)

Advertising Budget and Store Revenue: Chain Comparison

A retail company analyzed the effect of advertising spending (in thousands of dollars) on monthly st

Advertising Expenditure and Product Sales

An economist investigates whether advertising expenditure (in millions of dollars) predicts product

Bicycle Speed vs Oxygen Consumption

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

Biking Speed and Heart Rate

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

Coffee Consumption and Reaction Time Study

A study was conducted to examine the relationship between the number of cups of coffee consumed by c

Consumer Spending and Income Levels

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

Crop Yield and Fertilizer Application

An agronomist is examining how the amount of fertilizer applied (x, in kg) affects crop yield (y, in

Customer Wait Time and Satisfaction Ratings

A call center is analyzing whether average wait time ($$x$$, in minutes) affects customer satisfacti

Daily Temperature and Ice Cream Sales

A local ice cream shop manager investigates the relationship between daily high temperature (in °F)

Engine Size vs Highway Fuel Efficiency

An automobile researcher is studying the relationship between engine size (in liters) and highway fu

Hours of Sleep and Reaction Time

A study examines the effect of hours of sleep ($$x$$) on reaction time ($$y$$, in milliseconds) for

Hours of Training and Athletic Performance

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

Housing Price Estimation

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

Ice Cream Sales and Temperature

A food vendor tracked daily ice cream sales (in dollars) and the day's high temperature (in °F) over

Influence of Advertising Budget on Sales

A firm is investigating the effect of its advertising budget (in thousands of dollars) on weekly sal

Internet Speed vs. Streaming Delay

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

Machine Runtime and Maintenance Costs

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

Multiple Regression: Interpreting Slope in Presence of Collinearity

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

Plant Growth and Fertilizer Amount

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

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

Reaction Rate in Chemistry: Temperature and Reaction Time

An experiment investigates the effect of temperature (x, in °C) on reaction time (y, in seconds). Da

Regression Analysis in Judicial Decisions: Predicting Recidivism Risk Scores

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

Relationship Between Exercise Time and Cholesterol

A health study examines the relationship between weekly hours spent exercising (x) and cholesterol l

Social Media Use and Academic Performance

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

Temperature and Ice Cream Truck Sales

An ice cream truck owner analyzes the relationship between the daily temperature (x, in °F) and ice

Temperature Effects on Motor Speed

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

Weekly Internet Hours vs Exam Score Improvement

An education researcher collected data on the number of weekly hours students spent on the internet