AP Statistics FRQ Room

Analyzing z-Scores from a Frequency Distribution

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

College Admissions Test Scores

Test scores for a college admissions exam are approximately normally distributed with a mean of $$50

Customer Coffee Satisfaction Interval

A coffee shop surveys 50 customers to rate their satisfaction on a scale from 1 to 10. The sample ha

Daily Step Count Hypothesis Test

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

Dotplot Representation of Home Run Distances

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

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

Effects of Multiplicative Transformations on Test Scores

A data set representing test scores is given as follows: {45, 55, 67, 73, 82, 88, 90}. Answer the fo

Employee Turnover by Department

A company recorded employee turnover by department in a two-department organization (Sales and Engin

Examining Data Variability in Sports Statistics

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

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

Hospital Wait Time

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

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

Investigating Class Test Scores

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

Mobile Device Battery Life

The battery life of smartphones is normally distributed with a mean of $$10$$ hours and a standard d

Normal Distribution of Taxi Mileage

Taxicabs in a city are driven an average of $$75000$$ miles per year with a standard deviation of $$

Online Retail Customer Spending Analysis

An online retail store collects data on customer spending. In a sample of 60 customers, the mean spe

Salary Analysis: Effect of Raises on Mean Salary

A company has six employees whose current salaries are $$3000$$, $$7000$$, $$15000$$, $$22000$$, $$2

Sampling Distribution of the Sample Range for SAT Scores

A statistician is studying SAT scores whose distribution is known to have a certain degree of variab

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 Preference Survey Analysis

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

School Year Length Preferences Survey

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

Stock Price Trends Through Parallel Boxplots

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

Survey of Preferred Exercise Modalities

A fitness survey of 300 participants asked about their preferred type of exercise. The summary of re

University Lecture Attendance Analysis

A survey of university lecture attendances includes data from 28 lectures, with an average attendanc

Water Filtration Systems and Water Quality

A city planning department is studying the impact of different water filtration systems on the quali

Website Traffic: Click-Through Rate

An online advertisement is viewed by 250 visitors. Each visitor clicks the ad with a probability of

Athletic Performance Correlation Analysis

A study on athletes observed the relationship between hours of training per week (x) and competition

Calculation of Correlation and Linear Regression from Summary Statistics

A study examines the relationship between daily device usage (in hours, X) and a productivity score

City Bicycle Usage Study

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

Comparing Regression Lines for Calorie Consumption in Two Groups

A study compares the relationship between body weight (x) and calorie burn (y) for two groups: men a

Computing Regression Statistics from Summary Data: Advertising and Sales

A market research study investigates the relationship between advertising expenditure (X, in thousan

Consumer Product Satisfaction

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

Dietary Effects on Blood Pressure

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

Effectiveness of a New Curriculum

A school district implemented a new curriculum in some of its schools and maintained the traditional

Exploring the Sampling Distribution of the Regression Slope Under Increasing Error Variability

In a study of the relationship between income (x) and expenditure (y), researchers use simulation to

Local Policy Impact: Public Transportation and Commute Times

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

Market Research: Effect of Price on Sales Volume

A company is investigating how the price of their product affects its sales volume. The collected da

Medical Test Accuracy and Disease Prevalence

A certain disease affects 2% of the population. A diagnostic test for this disease has a sensitivity

Proof that the Mean of Residuals is Zero

Show mathematically that for a least squares regression model, the mean of the residuals is always z

Public Health Campaign on Smoking Cessation

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

Restaurant Tip Analysis

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

Reverse Regression: Predicting Hours Worked from Earnings

Consider a regression model for predicting earnings (Y, in thousands of dollars) from hours worked p

Sampling Distribution of Exam Scores

Exam scores at a college are normally distributed with a mean of $$75$$ and a standard deviation of

Scatterplot Analysis: Teen Social Media Usage

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

Simulation of Bivariate Data with Varying Leverage Effects on Regression Coefficients

A researcher simulates bivariate data to explore how the presence of high-leverage points affects th

Social Media Engagement Study

A social media analyst is comparing the level of high engagement on two platforms. The data collecte

Social Media Use and Online Privacy

In a study on digital behavior, participants were surveyed about their level of social media usage (

Student Study Habits Survey

A university conducted a survey examining the relationship between study habits and academic perform

Study Hours and Exam Scores

A high school collected data on the number of hours students studied for an exam (x) and their corre

Warehouse Shipping Times

Shipping times from a warehouse are normally distributed with a mean of $$4.5$$ days and a standard

Analyzing Student Study Habits

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

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

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 Prospective and Retrospective Data Collection in Education Studies

A school district wants to study the impact of extracurricular activities on academic performance. T

Comparing Retrospective and Prospective Studies in Outbreak Analysis

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

Comparing Sampling With and Without Replacement in Simulation

A researcher simulates sampling from a finite population of 200 units. Two methods are used to draw

Comparing Two Treatments in a Medical Study

A clinical trial compares two treatments for lowering blood pressure. Treatment A (n = 25) results i

Comparison of Test Preparation Courses on SAT Scores

A high school is comparing the effectiveness of two different test preparation courses on improving

Customer Satisfaction with New vs. Old Product

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

Designing a Representative Student Survey

A university desires to survey its 10,000 students about campus dining experiences. To ensure repres

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

Diet, Weight Loss, and Regression Analysis

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

Effect of Diet on Cholesterol Levels

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

Effectiveness of Stress Reduction Methods: Yoga vs. Meditation

A wellness center studied the effectiveness of yoga and meditation on reducing stress. In the yoga g

Effects of Diet Programs on Weight Loss

Researchers compared the effectiveness of two diet programs versus a Control group in achieving sign

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

Impact of Sample Size on Variability

In a study investigating average daily water consumption, two different sample sizes are used: one s

Investigating Voluntary Response Survey Bias

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

Participation in Extracurricular Activities

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

Public Health Intervention on Smoking Cessation

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

Sampling Methods in a Stratified Design

A researcher is studying the study habits of college students. The student population is divided int

Simulating Cluster Sampling and its Effects on the Sampling Distribution

A health survey is conducted using cluster sampling by selecting several schools from a district and

Systematic Sampling Implementation

A researcher intends to select 150 students from a high school of 1500 students using systematic sam

Urban Green Spaces and Air Quality

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

Using a Random Digit Table for Sampling

A school intends to randomly select 15 students from a list of 120 using a random digit table. Answe

Voting Patterns in a Retrospective Study

A retrospective study collected exit poll data to determine the level of support for Policy X among

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

Carnival Game Payoff Transformation

In a carnival game, the possible winnings are $$2$$ dollars with probability $$0.5$$, $$5$$ dollars

Comparing Average Test Scores of Two Teaching Methods

A study compares the effectiveness of two teaching methods in a school. Traditional teaching was use

Comparing Guessing and Knowledge-based Answers

In an exam, if a student guesses an answer, the probability of a correct response is 0.20. If the st

Comparing Manufacturing Processes for Defect Reduction

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

Daily Steps and Calorie Burn Regression Analysis

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

Defective Products in Quality Control (Binomial Distribution)

In a quality control process, each product has a defect probability of 0.08 and is inspected indepen

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

Game of Score Sums

Two friends play a game where Friend A draws a card with values {2, 4, 6} (each equally likely) and

Geometric Distribution in Reliability Testing

A machine in a factory has a 5% chance of failing on any given day. Let $$X$$ denote the day on whic

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 Productivity Analysis

The daily output of highway construction (in miles) depends on weather conditions as follows: | Wea

Highway Worker Productivity

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

Household Income and Entertainment Expenditure Regression Analysis

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

Insurance Policy Sales Analysis

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

Law of Large Numbers in Coin Toss Games

Consider a game where a player repeatedly flips a fair coin. The game has two winning conditions: In

Medical Screening Test Accuracy by Gender

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

Movie Rating Analysis on Streaming Platforms

A survey was conducted to compare negative movie ratings on two streaming platforms. On Platform A,

Online Learning vs. Traditional Classroom Formats

An educational researcher is studying the effectiveness of online learning compared to traditional c

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

Simulated Coin Toss Sampling Distribution

In a simulation experiment, you simulate flipping a fair coin multiple times to record the proportio

Simulation Analysis of Measurement Process Reliability

In a laboratory setting, a measurement instrument with known error characteristics is used to record

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 Post Engagement

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

Store Customer Satisfaction Survey

A popular retail store conducted a survey to measure customer satisfaction. Out of 120 randomly sele

Testing Customer Satisfaction Claims

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

The Impact of Sample Size on Outcome Predictability

A game organizer is designing a carnival game that involves tossing a fair coin. A player wins if th

Tip Amounts from Different Meal Services

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

University Admissions Multistage Process

A university's admissions process consists of two independent stages. A student first undergoes a sc

Urban Traffic Volume and Air Quality

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

Weather Impact on Road Conditions

A study of road temperatures under different weather conditions produced the following results. Use

Assessing the Conditions for the Central Limit Theorem

A production facility records the number of widgets produced per day by a machine. The daily product

Bacterial Count in Water Samples

A water quality test measures the concentration of bacteria (in CFU per 100 ml) in a river. The popu

Battery Life Analysis Using Normal Distribution

A battery manufacturer claims that the lifespan of its batteries is normally distributed with mean $

Caffeine Content in Energy Drinks

A particular energy drink contains an average of $$200$$ mg of caffeine with a standard deviation of

Car Engine Performance Analysis

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

Comparing Biased Estimators via Simulation Outcomes

A simulation study compares two estimators for a population parameter. Estimator A has a constant bi

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

Effect of Sample Size on Variability

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

Environmental Study: Tree Heights

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

Evaluating Customer Satisfaction Proportions

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

Evaluating Manufacturing Estimators

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

Evaluating Math Anxiety and Brain Activity

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

Impact of Devices on Online Purchases

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

Interpreting p-values in a Clinical Trial

In a clinical trial testing a new drug, the null hypothesis states that the drug has no effect. The

Math Anxiety Brain Activity Proportions

It is estimated that $$80\%$$ of individuals with high math anxiety exhibit brain activity similar t

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 $$5$$

Sample Variance Distribution in Produce Weights

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

Sampling Distribution for Sample Proportions in a Survey

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

Simulated Sampling Distribution for Rare Events

A rare genetic marker is present in only 1% of a large population. A random sample of 200 individual

Simulation of Sampling Distributions: Dreams Recorded

A study finds that high school students remember an average of 3.4 dreams per night with a variance

Simulation Study of Income Medians

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

Simulation Study on Sample Variances

A simulation study is conducted to explore the sampling distribution of the sample variance $$s^2$$

Student Test Scores Sampling Distribution

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

Training Techniques and Marathon Finish Times

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

Widget Lifespan Quality Control

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

Campaign's Voter Turnout Comparison

A political campaign is studying voter turnout in two neighboring cities. In City A, a survey of 400

Conservation Program Study

A local government has implemented an environmental conservation program intended to increase the pr

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 Preference Difference Between Cities

A regional chain surveys customers in two cities regarding their preference for a new product. In Ci

Customer Satisfaction Survey

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

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

Effectiveness of a Drug

A clinical trial is conducted to test the effectiveness of a new drug. In the trial, 400 patients we

Effectiveness of a Public Health Intervention: Investigative Task

A public health organization is assessing the effectiveness of a new intervention aimed at increasin

Election Poll Margin of Error Analysis

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

Evaluating 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

Evaluating Strike Support

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

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

Healthcare Plan Satisfaction

A survey was conducted among employees to assess satisfaction with their healthcare plans. Participa

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.

Marketing Strategies: Hypothesis Testing for Two Proportions

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

Public Health Confidence Interval

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

Quality Control in Manufacturing

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

Retail Coupon Usage Among Customers

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

Retail Store Customer Satisfaction Confidence Interval

A retail store conducted a customer satisfaction survey. A random sample of n = 400 customers was se

Sample Size and Margin of Error Trade-Off Analysis

A political analyst is planning a poll and is considering two sample sizes. One sample of 300 respon

Sampling Distribution and Confidence Intervals for Proportions

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

Service Reliability Study Analysis

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

Smoking Status and Respiratory Illness

Hospital records show data on patients' smoking status and whether they have a respiratory illness.

Sports Participation by Gender and Sport Type

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

Survey Analysis: Confidence Interval for College Students' Online Class Preference

A survey of college students was conducted to estimate the proportion of students who prefer online

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 a Rare Event Proportion

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

Type I and Type II Errors in a Drug Trial

In a clinical trial of a new drug, the null hypothesis states that the drug's side effect rate is 10

Vaccine Hesitancy Survey Design

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

Advertising Budget and Sales Performance Analysis

The scatterplot below represents data on a company's monthly advertising budget (in thousands of dol

BMI and Systolic Blood Pressure Analysis

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

Coffee and Exam Performance

A university study collected data on whether students drink coffee and their exam performance. The t

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

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

Daily Steps: Wearable Device Analysis

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

Dosage Effect on Symptom Reduction

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

Effect of Medication on Blood Pressure: Paired Data Analysis

A study was conducted on 30 patients to evaluate the effect of a new medication on systolic blood pr

Effectiveness of Drug Treatments

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

Effectiveness of Tutoring Program Investigation

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

Election Polling Power Analysis

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

Enzyme Activity Confidence Interval

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

Fuel Consumption and Distance Traveled Analysis

The scatterplot below displays data on the gallons of fuel used (x-axis) and the corresponding dista

Hospital Stay Duration Comparison

A hospital administration is examining the average length of patient stays in two independent units:

Impact of New Traffic Signals on Commute Times

A city installs new traffic signals at a busy intersection to improve traffic flow. Traffic engineer

Income Analysis for a Tech Company

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

Machine Downtime Analysis

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

Manufacturing Measurement Variability

A quality control procedure involves monitoring the variability in a product's critical dimension us

Medical Test Accuracy and Diagnosis

A hospital is assessing the accuracy of a diagnostic test that indicates 'Positive' or 'Negative' re

Quality Control: Machine Calibration

A factory employs a machine to produce metal rods. To check the machine’s calibration, two samples o

Simulating Sampling Distribution of Chip Weight

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

Simulating the Sampling Distribution of Mean Light Bulb Lifetimes

A manufacturer runs a simulation to generate the sampling distribution of the sample mean lifetime f

Simulation of Sampling Distribution of Mean Reaction Times

In a cognitive psychology study, reaction times (in milliseconds) to a stimulus are collected. A sim

Study Hours and GPA Analysis

The scatterplot below shows data on college students' weekly study hours (x-axis) and their GPA (on

Study on Exam Anxiety Reduction

A psychologist investigates the effect of a relaxation technique on test anxiety. Twenty-five studen

Weekly Hours Worked and Earnings Analysis

The scatterplot below displays data relating weekly hours worked (x-axis) to weekly earnings in doll

Wind Speed Measurements: Station Upgrade Impact

A weather station upgrades its sensors and collects paired wind speed measurements from before and a

Workplace Wellness Program Evaluation

A company evaluates its workplace wellness program by comparing the health outcomes of employees who

Analysis of Product Defects in a Manufacturing Process

A manufacturing process produces parts that can fall into one of four categories based on defect typ

Animal Species Distribution in Habitats: Chi-Square Test

Researchers collected counts of three animal species (Deer, Rabbit, Fox) in two habitats. The counts

Branch Service Quality

A bank is comparing customer satisfaction across its three branches. Each branch serviced 100 custom

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 Satisfaction Survey Across Store Locations

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

Distribution of Housing Types in a City

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

Effectiveness of a New Training Program across Branches

A company implements a new training program in three of its branches. After the program, employees a

Examining Political Ideology: Chi-Square Test for Homogeneity

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

Fair Dice Rolling Goodness-of-Fit Test

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

FRQ 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

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

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

Goodness-of-Fit for Beverage Preferences

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

Homogeneity in Customer Service Satisfaction Across Branches

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

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

Investigative Analysis: Public Health Awareness Survey

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

Job Satisfaction Among Different Occupations

A study is conducted to compare job satisfaction among four occupational groups in a school system:

Marketing Strategy Effectiveness

A company wants to assess if customer responses vary by the type of advertisement. Three ad types (O

Pet Ownership and Residence Type Independence Test

A city survey collected data on pet ownership (Owning a pet, Not owning a pet) and type of residence

Restaurant Choices Across Regions: Chi-Square Test for Independence

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

Smoking and Lung Disease: Independence Test

A survey of 300 individuals reports the following counts: Smoker with lung disease = 40, Smoker with

Species Distribution in a Wildlife Reserve

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

Sports Participation and Gender – Chi-Square Test for Independence

A school conducted a survey to examine the relationship between gender (Male, Female) and participat

Travel Mode and Environmental Concern – Chi-Square Test for Independence

A survey of 250 commuters collected data on their primary travel mode (Car, Public Transit, Bike) an

Voting Patterns and Ballot Measure Support

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

Workplace Safety Incidents: Chi-Square Test for Independence

In a manufacturing plant, data on safety incidents are collected and classified by type (Minor, Seri

Advertising Spending and Sales Revenue

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

Altitude and Cooking Time

Researchers are studying the effect of altitude ($$x$$, in meters) on cooking time ($$y$$, in minute

Car Mileage and Tire Pressure

A car manufacturer wants to study the effect of tire pressure (x, in psi) on car mileage (y, in mile

Coffee Consumption and Alertness

A researcher investigated the relationship between daily coffee consumption (measured in cups) and a

Coffee Consumption and Alertness

Researchers are investigating the relationship between the number of cups of coffee consumed per day

Effect of Class Size on Student Achievement

An education researcher examines data from 50 classrooms to study the relationship between class siz

Effect of Study Intervention on Academic Performance

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

Effect of Study Time on Test Scores

A teacher collects data on the number of hours studied (x) and exam scores (y) out of 100 for 25 stu

Employee Performance from Experience

An HR department collected data on 28 employees to understand how years of experience (x) affect per

Employee Salary and Years of Experience

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

Energy Consumption Analysis

A utility company is investigating the relationship between outside temperature (in °F) and resident

Energy Consumption and Temperature: Simulation Study

A data analyst is investigating the relationship between ambient temperature (in $$^\circ C$$) and h

Evaluating the Impact of Work Experience on Promotion Rate

An organizational study examines whether years of work experience (x) affect the promotion rate (y,

Exercise Frequency and Resting Heart Rate

A fitness study collected data from 50 adults on the number of times they exercise per week and thei

Fuel Efficiency and Car Weight

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

Height and Weight Relationship: Male vs Female

A study investigates the relationship between height (in inches) and weight (in pounds) among male a

Hours of Training and Athletic Performance

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

House Prices and Square Footage

A real estate study uses the square footage of houses (x, in square feet) to predict their prices (y

Industrial Emissions and Air Quality

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

Manufacturing Quality Control: Regression Parameter Optimization Simulation

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

Marketing Strategy and Customer Visits

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

Modeling Blood Pressure Response to Medication Dosage

A medical study investigates the effect of medication dosage (x, in mg) on the reduction in systolic

Online Advertisement View Time and Purchase Likelihood

A study examines the relationship between the time spent viewing an online advertisement ($$x$$, in

Online Engagement and Sales Conversion

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

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

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

Software Development Efficiency: Lines of Code and Bug Count

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

Weather Forecasting: Humidity vs. Chance of Precipitation

Meteorologists studied the relationship between relative humidity (x, in percentage points) and chan

Weekly Internet Hours vs Exam Score Improvement

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