AP Statistics FRQ Room

Analysis of Categorical Data from Elections

A recent survey sampled 1000 voters to determine their preferred candidate in a local election. The

AP Enrollment in High School

A survey of 2200 high school seniors recorded the number of AP classes each student is taking. The d

Bus Scheduling and Commuter Wait Times

A city transit authority is investigating whether optimizing bus schedules can reduce average commut

Cafeteria Food Satisfaction Proportion

A college cafeteria conducted a survey to estimate the proportion of students who are satisfied with

College vs. High School Sleep Study

Two surveys measured the number of hours of sleep per night. The high school survey recorded the fol

Comparing Cumulative Frequency Graphs for Age Distributions

Two cumulative frequency plots represent the age distributions of residents in a town for the years

Cumulative Frequency Analysis of Age Distribution

A study compares the age distributions of two different years using cumulative frequency plots. In Y

Delivery Time Hypothesis Test

A fast-food chain advertises that its average delivery time is $$36$$ minutes. A consumer group coll

Dietary Preferences by Gender

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

Distribution of Heights in a Grade

A study on the heights (in centimeters) of students in a particular grade produced the following fre

Effect of Fertilizer Types on Tomato Yield

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

Effectiveness of a New Drug

A clinical trial is conducted to evaluate the effectiveness of a new drug in improving patient outco

Effectiveness of a New Wearable Heart Rate Monitor

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

Employee Salary Adjustments

A company’s six employee salaries (in dollars) are as follows: {3000, 7000, 15000, 22000, 23000, 380

Error Rates in Two Production Machines

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

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

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

Holiday Shopping Behavior: In-Store vs Online

During the holiday season, a survey was conducted on shopping behavior. Among 300 in-store shoppers,

Hospital Wait Time

In an emergency room (ER), patient wait times in minutes are normally distributed with a mean of $$4

Impact of Incentives on Survey Participation

A market survey was carried out with two groups: one received an incentive and the other did not. In

Internet Usage Among College Students

A survey of 220 college students recorded the number of hours they spend online per day. The results

Interpreting a Dot Plot of Daily Coffee Consumption

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

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

Public Opinion on School Length: Categorical Data Summary

In a survey of 2000 parents regarding their preference for the length of the school year, the respon

Sampling Distribution of Average Purchase Amount

Individual consumer purchase amounts are normally distributed with a mean of $$50$$ dollars and a st

Sampling Distribution of the Median in a Skewed Production Process

A factory produces components whose lifespans (in hours) are right-skewed due to occasional defects.

School Survey on Categorical Preferences

A high school conducted a survey of 400 students regarding their preferred school day length. The re

School Year Length Preferences Survey

A survey is conducted among 2000 parents regarding their preferred school year length. The frequency

Shopping Satisfaction: Online vs. In-Store

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

Sleep Deprivation and Reaction Times

A behavioral study is designed to examine the effect of sleep deprivation on reaction times. Partici

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}.

Test Scores Histogram Interpretation

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

University Course Selection by Gender

A university survey of 300 students recorded their course selection (STEM or Humanities) and gender

Weekly Exercise Sessions

Assume that on any given day, a person exercises for at least 30 minutes with a probability of $$0.4

Analysis of Influential Points in Athlete Performance Data

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

Assessing Impact of Transformation on Regression: Log Transformation Example

A data set recording car engine sizes (in liters, X) and corresponding fuel efficiency (in mpg, Y) s

Comparing Two Online Learning Platforms

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

Customer Return Rates for Two Brands

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

Customer Service Evaluation: Categorical Analysis

A retail chain surveyed 300 customers regarding their overall satisfaction (Satisfied or Dissatisfie

Employee Training Effectiveness

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

Environmental Awareness Survey

A survey was conducted to explore the relationship between recycling habits and environmental concer

Evaluating Coefficient of Determination in Athletic Performance

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

Fitness Tracker Analysis

A fitness center collected data from individuals using fitness trackers, recording daily steps (x) a

Forest Fire Risk Analysis

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

Free Throw Performance in Basketball

A basketball player has a true free throw success rate of $$80\%$$. In one game, the player attempts

Housing Prices and Square Footage Analysis

A real estate analyst collected data on various houses regarding their square footage (in square fee

Impact of Skewness on the Sampling Distribution of the Sample Mean in Bivariate Data

A researcher collects data on household income (x) and spending on luxury goods (y), noting that inc

Public Health Campaign on Smoking Cessation

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

Restaurant Order Survey

A restaurant surveyed 140 customers to see if there was any association between meal type (Vegetaria

Restaurant Tip Analysis

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

Simulation Study for Confidence Intervals in Linear Regression Predictions

A marketing analyst uses simulation to assess the performance of confidence intervals in predicting

Startup Revenue Growth

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

Study Time and Test Scores Relationship

A teacher collected data on the number of hours 25 students studied for a final exam and their corre

Tech Company Productivity Analysis

A tech company collected data on the number of programming hours (x) and the number of bugs fixed (y

Voting Behavior and Media Consumption

A political analyst surveyed 300 individuals to study the relationship between media consumption and

Willingness to Adopt Electric Vehicles

A market research study investigated whether income level influences the willingness to adopt electr

Analysis of Recycling Behavior

A survey was conducted to study recycling habits among individuals with different education levels.

Community Fitness Program and Weight Loss

A local government launches a community fitness program to help residents lose weight. The program i

Commute Time and Job Satisfaction

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

Comparing Disease Incidence in Two Regions

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

Comparing Retrospective and Prospective Studies in Outbreak Analysis

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

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

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

Double-Blind Experiment Design for Nausea Reduction

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

Effect of Noise Levels on Sleep Quality

An environmental study investigates the association between ambient noise level (in decibels, x) and

Effect of Outliers on Sampling Distributions

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

Evaluating a New Teaching Method

A study compares a traditional teaching method and a new teaching method. In an independent study, 3

Impact of Sample Size on Confidence Interval Width

Consider two studies estimating the mean of a population, both with a known population standard devi

Manufacturing Processes and Product Lifespan

A manufacturing company is testing whether a new production process can increase the lifespan of its

Matched Pairs Experiment for Diet and Exercise in Blood Pressure Study

Researchers are studying the effects of two different diets combined with varying exercise regimens

Measurement Reliability in Climate Data Collection

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

Music Therapy and Stress Levels

A study is designed to test whether music therapy can reduce stress levels in adults. A double-blind

Predicting Blood Pressure from Age: Regression and Inference

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

Simulation of the Sampling Distribution of the Sample Variance

A researcher runs a simulation to approximate the sampling distribution of the sample variance from

Traffic Flow Analysis

A transportation department uses systematic sampling to count the number of vehicles passing a check

Urban Green Spaces and Air Quality

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

Ad Spend and Market Share Regression Analysis

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

Apartment Rental Prices Estimation

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

Applying Chebyshev's Inequality in Quality Control

A production process yields items with an average weight of 50 grams and a standard deviation of 5 g

Binomial Distribution in Lightbulb Defectiveness

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

Casino Free Chips Expected Sum

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

Charity Lottery Expected Value Calculation

A charity holds a lottery selling 10,000 tickets at $$1$$ each. One ticket wins a prize of $$7500$$.

Coin Flip Game Strategies

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

Comparison of Accident Rates on Highway Sections

A study on highway safety compared accident rates on two sections of a highway. On Section A, 5 acci

Effectiveness of Public Health Announcements on Mask-Wearing Behavior

During a flu outbreak, a health department launches a public health campaign to encourage mask-weari

Employee Turnover Comparison in Two Departments

A company collected data on employee retention in two departments. In Department X, 45 out of 60 emp

Fitness Center Membership Duration

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

Fitness Class Participation by Age Group

A gym surveyed 300 members about their preferred fitness class types. The results by age group are d

High School SAT Scores Analysis

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

Highway Construction Work Analysis

A highway engineer observes that on a clear day, workers can lay $$5$$ miles of highway; on a rainy

Insurance Policy Sales Analysis

An insurance salesperson records her daily sales of auto and home insurance policies. The probabilit

Manufacturing Process Downtime

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

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 widgets, each having an independent 5% chance of being defective. Quality control

Raffle Ticket Payouts in a Fundraiser

A charity raffle sells 500 tickets at $2 each. There is one main prize of $800 and two smaller prize

Rare Defects and Poisson Approximation

A factory produces electronic components with a defect rate of 0.002. In a shipment of 2000 units, l

Reading Preferences by Genre and Format

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

Restaurant Orders by Meal Type and Tip Size

A restaurant collected data on tip sizes based on whether the order was dine-in or take-out. The res

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

Sleep Duration and Reaction Time Regression Analysis

A study looks at how sleep duration (in hours) affects reaction time (in milliseconds) on a computer

Smartphone Usage and Sleep Quality Regression Analysis

A study investigates whether the number of hours spent on a smartphone before bedtime affects sleep

Social Media Usage Patterns by Age Group

A study surveyed 300 social media users to determine their preferred platform. The respondents were

Student Test Scores and Conditional Probabilities

A school's data on test strategies and score ranges is summarized in the tables below. Table 1: Str

Television Viewing Habits by Age and Time of Day

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

Tip Amounts from Different Meal Services

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

Traffic Accident Analysis

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

Urban Traffic Volume and Air Quality Regression Analysis

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

Virus Spread Modeling among Animal Species

A study examines the spread of a virus among three animal species with the following data: | Specie

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

Assessing Estimators for Baseball Weight

A manufacturer is evaluating five different estimators for the weight of professional baseballs. The

Caffeine Content Analysis

An energy drink has a caffeine content that is normally distributed with mean $$\mu = 150$$ mg and s

Caffeine Content Analysis in Energy Drink Boxes

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

College Major and Internship Experience

A university conducted a survey on students' internship experiences across different majors. The tab

Comparing Juice Bottling Process

A juice company compares its bottling process with that of a competitor. A random sample of 50 bottl

Effect of Sample Size on Standard Error

Consider a population with a standard deviation of $$\sigma = 12$$. Samples are drawn to estimate th

Evaluating Customer Satisfaction Proportions

A restaurant chain wants to compare customer satisfaction between two of its locations. At Restauran

Genetic Mutations in New Fathers

A study estimates that 40-year-old men contribute an average of $$65$$ genetic mutations (with a sta

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

LED Lightbulb Lifespan Probability Analysis

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

Quality Control in Manufacturing: Sampling Distribution of Mean Weight

A factory produces metal rods with a mean weight of $$100$$ grams and a standard deviation of $$5$$

Smartphone Battery Life Comparison

A technology review compared the battery life of two smartphone models. Model X was tested with 60 p

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

Analyzing Proportions as a Function of Batch Size

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

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

Coffee Preference by Age Groups

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

Coffee Shop Loyalty

A coffee shop chain is investigating customer loyalty. A survey at the downtown branch (Group A) sam

Comparative Study on Voter Turnout in Urban and Rural Areas

A study was conducted comparing voter turnout in urban and rural areas. In an urban sample of 400 re

Confidence Interval for Proportion in Market Research

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

Confidence Interval for Social Media Users

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

Consumer Preference: Hypothesis Testing for a Single Proportion

A company claims that at least 40% of consumers prefer its new product. In a sample of 250 consumers

Consumer Product Hypothesis Test

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

Customer 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

Diet Choices by Gender

A survey was conducted to analyze diet choices among male and female participants. Participants were

Drug Efficacy in Clinical Trials

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

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

Evaluating a Confidence Interval in a Political Poll

A political poll of 1,000 registered voters finds that 540 support candidate A. Pollsters wish to cr

Health Study: Smoking Prevalence Comparison

A health study compared the smoking prevalence between two cities. In City A, a sample of 500 respon

Health Survey Confidence Interval Analysis

A local health department conducted a survey regarding residents' compliance with a new health regul

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

Impact of New Educational Program

A school district implemented a new teaching method aimed at improving student performance. In a stu

Impact of Training Program on Certification Rates

A company implemented a training program to improve certification rates among its employees. In a ra

Online Shopping Proportion Analysis

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

Political Campaign Support Analysis

A political campaign conducted a survey to determine support for a candidate. In the survey, a simpl

Product Return Rates by Category

A retail store analyzed product return rates for different categories. Products are classified into

Public Health Confidence Interval

A hospital conducted a simple random sample of 500 patients to gauge satisfaction with treatment qua

Service Reliability Study Analysis

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

Significance Testing of Proportion Differences in Crime Rates

In a survey, 55 out of 200 residents in City A and 40 out of 250 residents in City B reported feelin

Smartphone Brand Preference by Income Level

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

Test of a Hypothesis on Voter Turnout

A political analyst claims that at least 60% of registered voters participate in elections. A sample

Testing for Change in Voter Intent Over Time

An exit poll conducted before and after a major debate shows different levels of support for Candida

Accident Rates Comparison Between Departments

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

Analyzing Machine Production Tolerances

In a manufacturing process, 15 measurements of a product dimension are recorded. The sample has a me

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

BMI and Systolic Blood Pressure Analysis

The scatterplot below shows data on body mass index (BMI, x-axis) and systolic blood pressure in mmH

Career Development Program

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

Comparative Analysis of Daily Sales at Two Branches

Two branches of a store report their average daily sales. Branch A has a sample of $$n=30$$ with a m

Comparative Analysis of Lecture Techniques Using Paired Data

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

Comparing 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 Manufacturing Processes

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

Comparison of Waiting Times: Urban vs. Rural Hospitals

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

Customer Satisfaction Survey

A company wants to evaluate customer satisfaction with two service channels: Online Chat and Telepho

Daily Steps: Wearable Device Analysis

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

Diet Choice and Energy Levels

A nutritionist investigates whether there is an association between diet type (Vegetarian vs. Omnivo

Effect of a New Fertilizer on Crop Yield

An agricultural researcher investigates the effect of a new fertilizer on the yield of a particular

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

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 Variability on Confidence Intervals: A Simulation Study

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

Light Bulb Lifespan Hypothesis Test

A company advertises that its light bulbs have an average lifespan of 1200 hours. A quality control

Machine Calibration Paired Data

A manufacturer tests the effect of a maintenance update on machine calibration. Fifteen machines are

Machine Downtime Analysis

A manufacturing plant monitors the daily downtime (in minutes) of a critical machine. Over 40 indepe

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

Monthly Sales Performance Analysis

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

New Coffee Blend and Alertness Test

A beverage company is testing whether a new coffee blend improves alertness by reducing reaction tim

Online Platform User Engagement

An online platform wants to compare the average daily time spent by users in two different regions.

Project Completion Times

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

Public Transportation Use and Environmental Awareness

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

Quality Control Analysis using Simulation-Based P-Value

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

Reaction Time Hypothesis Test

A psychologist wishes to test a manufacturer's claim that the average driver reaction time is \(0.8\

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 Mean Crop Yield

An agricultural researcher is interested in the average crop yield (bushels per acre) of a particula

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 with Measurement Error

A lab is troubleshooting a sensor that measures the weight of produced components. A simulation is c

Sleep Duration and Reaction Time Analysis

The scatterplot below shows data on hours of sleep (x-axis) and reaction time in seconds (y-axis) fr

Technology Adoption in Businesses

A market analysis explores the relationship between company size and the adoption of new technology.

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

Training Hours and Employee Productivity Analysis

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

Yearly Comparison of Mathematics Test Scores

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

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 for Disease Rates

A health researcher claims that the incidence of a particular disease in a population is distributed

Customer Satisfaction Across Regions

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

Customer Satisfaction Survey Across Store Locations

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

Dice Fairness Goodness-of-Fit Test

A game designer claims that a six-sided die is fair, such that each face appears with probability $$

Effect of Marketing Campaign on Brand Awareness

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

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

Examining Political Ideology: Chi-Square Test for Homogeneity

A political scientist collected data on ideological self-identification (Liberal, Moderate, Conserva

Favorite Ice Cream Flavor Goodness-of-Fit Test

A market survey hypothesizes that the favorite ice cream flavors are distributed as: Chocolate 40%,

FRQ 17: Customer Complaint Types and Resolution Outcomes

A company categorizes customer complaints into three types: Billing, Service, and Product Quality. E

Game Outcome Distribution

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

Investigative Analysis: Public Health Awareness Survey

A public health department conducts a multi-stage survey to assess health awareness among residents

Learning Style and Major Association Independence Test

A college survey of 300 students categorized them by their preferred learning style (Visual, Auditor

Manufacturing Defect Distribution Goodness-of-Fit

A factory produces items that may have one of four types of defects: Type A, Type B, Type C, and Typ

Participation in Extracurricular Activities: Chi-Square Test for Homogeneity

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

Political Party and Environmental Concern

A survey studies the relationship between political party affiliation (Democratic, Republican, Indep

Product Packaging Preference Across Regions

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

Product Preference Independence Test by Gender

A survey of 200 participants gathered data on product preference among four options (Product A, B, C

Robustness of Chi-Square Test: Small Expected Counts

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

Smartphone Brand Preference

A market research firm expects that smartphone brand preferences will follow the proportions: Brand

Smoking and Exercise Frequency Independence Test

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

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

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

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

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

Transportation Mode Among City Residents

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

Voter Turnout by Age Group Homogeneity Test

A political scientist wants to compare voter turnout (Yes, No) across three age groups: Young, Middl

Voting Methods: Chi-Square Goodness-of-Fit

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

Voting Patterns and Ballot Measure Support

A survey of 400 voters categorizes responses by party affiliation and support for a ballot measure.

Advertising and Sales Revenue Regression Analysis

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

Advertising Expenditure and Product Sales

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

Advertising Reach and Customer Acquisition

A digital marketing analyst studies the relationship between the number of advertising impressions (

Advertising Spending and Sales Revenue

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

Coffee Consumption and Alertness

A study examines the relationship between cups of coffee consumed per day (x) and a measured alertne

Crop Yield and Fertilizer Application

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

Crop Yields and Fertilizer Usage

Agricultural researchers are investigating the effect of fertilizer amount (in kg per hectare) on cr

E-Commerce Website Traffic and Sales

An online retailer analyzes the relationship between daily website traffic (in thousands of visits)

Elevation and Atmospheric Pressure

Atmospheric scientists study the relationship between elevation ($$x$$, in meters) and atmospheric p

Engine Temperature and Efficiency Loss

An engineering study investigates the effect of engine temperature ($$x$$, in $$^\circ C$$) on effic

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

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

Fuel Efficiency and Car Weight

An automotive researcher is examining the relationship between a car's weight (in pounds) and its fu

Hours of Sleep and Reaction Time

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

Industrial Emissions and Air Quality

A governmental agency is evaluating the impact of industrial emissions (x, in tons per day) on local

Measurement Error Impact on Slope Estimation: Simulation Study

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

Medical Dosage and Blood Pressure Reduction

A clinical study examines the effect of a new drug dosage (x, in mg) on the reduction of blood press

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

Predicting Student Performance with Attendance Rates

A teacher collects data on student attendance rates (x, in percentage) and corresponding performance

Regression Analysis in Real Estate Pricing

This question examines inference for the slope in a linear regression analysis between living area (

Relationship Between Stress Level and Reaction Time

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

Relationship Between Temperature and Energy Consumption

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

Replicating Slope T-Test Using Summary Statistics

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

Robotics and Efficiency

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

Sleep Hours and Cognitive Performance

A study examines the effect of sleep hours (x) on cognitive performance (y, measured as a test score

Sleep Hours and Reaction Time

A psychology experiment studies the effect of sleep duration (in hours) on reaction time (in millise

Study Abroad Duration and Language Proficiency

A language institute studies the effect of time spent abroad (x, in months) on language proficiency

Tree Growth Analysis: Simulated Slope Distribution

An ecologist is studying the relationship between the age of trees and their heights. The ecologist

Years of Experience and Salary Increase

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