AP Statistics FRQ Room

Advertisement Design Impact on Customer Recall

A marketing company wants to test whether two different advertisement designs lead to differences in

AP Music Tastes Survey

A survey of 320 students about their favorite music genre produced the following data: | Genre

Bootstrap Simulation of the Sampling Distribution of the Median Salary

Given the salary data $$\$3000$$, $$\$7000$$, $$\$15000$$, $$\$22000$$, $$\$23000$$, and $$\$38000$$

Comparing Sampling Distributions from Populations with Different Variances

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

Comparing Sleep Hours: High School vs College

Two surveys were conducted comparing the nightly sleep hours of high school and college students. Th

Daily Step Count Hypothesis Test

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

Effects of Adding a Constant on Measures of Spread

Consider the dataset of exam scores: {65, 70, 75, 80, 85}. Answer the following:

Empirical Rule Verification via Simulation

A professor is studying exam scores that are normally distributed with a mean of 70 and a standard d

Evaluating a Histogram for Skewness in Temperature Data

A histogram shows the distribution of daily temperatures (in °F) during a summer month. The histogra

Favorite School Lunch Choices

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

First Defective Product: Geometric Distribution

In a factory, each product has a 3% chance of being defective. Products are inspected sequentially u

Holiday Shopping Behavior: In-Store vs Online

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

Internet Usage Among College Students

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

Marketing Campaign Reach by Region

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

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

Normal Distribution: Taxi Mileage

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

Relative Frequency Calculation from Pet Ownership Survey

A survey regarding pet ownership in households produced the following frequency table: | Pets Owned

Restaurant Preference and Time Slot

A survey of 200 diners asked about their restaurant choice (Restaurant A or Restaurant B) and the ti

Simulation and Transformation Effects on the Sampling Distribution

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

Sports Participation and Club Membership

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

Studying Daily Step Counts from a Fitness App

A fitness app recorded the number of steps taken per day by its users. The data were grouped into th

Survey of Smartphone Usage Time

A survey of 500 students categorized their daily smartphone usage (in hours) with the following data

Survey Response Methods Comparison

A survey was administered using two methods: telephone and online. In the telephone survey, 115 out

Teacher Ages Analysis

The ages (in years) of 12 mathematics teachers are: $$\{24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 54,

Test Scores Histogram Interpretation

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

Voting Behavior by Education Level

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

Analysis of Two Categorical Variables in a School Survey

A high school surveyed 300 students to determine their favorite subject (Mathematics, Science, or En

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

A data analyst uses the bootstrap method to approximate the sampling distribution of the regression

City Bicycle Usage Study

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

Complex Survey Analysis: Income and Expenditure Patterns

A national survey collects data on household income (in US dollars) and monthly expenditure (in US d

Computing Regression Statistics from Summary Data: Advertising and Sales

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

Correlation and Coefficient of Determination in Exam Performance

A researcher studying exam performance collected data on the number of hours students studied (X) an

Customer Satisfaction Comparison at Two Store Branches

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

Designing an Observational Study: Screen Time and Sleep Quality

You are tasked with designing an observational study to investigate the relationship between daily s

Effect of Advertisement Frequency on Brand Recognition

A marketing study was conducted to analyze the relationship between the number of advertisements see

Elderly Health Program Evaluation

An evaluation was carried out to assess whether participation in a health program by elderly individ

Evaluating Sales Team Performance

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

Examining the Sampling Distribution of the Mean Difference in Two Groups via Simulation

A researcher collected test scores from two different classes with 30 students each. She wants to si

Exploring Temperature and Ice Cream Sales

A study was conducted to explore the relationship between daily temperature (in °F) and ice cream sa

Geometric Distribution of Quick Transactions at a Bank

At a bank teller, the probability that a customer completes a transaction in less than 5 minutes is

Housing Renovation Impact on Property Values

A real estate researcher is investigating whether the cost of home renovations (x, in thousands of d

Impact of a New Study App on Academic Performance

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

Least Squares Regression for Predicting House Prices

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

Marketing Survey: Advertising Budget vs. New Customers

A marketing survey collected data on weekly advertising budget (x, in thousands of dollars) and the

Medical Test Accuracy and Disease Prevalence

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

Online Course Engagement and Performance

In an online course, data were collected from 40 students on the number of forum posts (x) and final

Pets and Stress Levels

A study investigated the relationship between the number of pets owned (x) and self-reported stress

Public Health Campaign on Smoking Cessation

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

Residual Analysis in House Price Prediction

A real estate analyst develops a linear regression model to predict house prices (in $1000s) from ho

Simulation Study of the Sampling Distribution of the Correlation Coefficient

Researchers are interested in studying the correlation between two variables, X and Y. To assess the

Social Media Engagement Analysis

A study examines the relationship between the number of posts an individual makes per day (x) and th

Social Media Use and Online Privacy

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

Study Hours and Exam Scores

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

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

Training Hours and Error Rates in Manufacturing

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

Transformation to Achieve Linearity: Population Growth

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

Voter Turnout by Gender

A political survey was conducted to study voter turnout by gender. The survey recorded whether respo

Analysis of Recycling Behavior

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

Analyzing Sampling Variability Using Boxplots

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

Cluster Sampling in Educational Testing

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

Consumer Preferences for Coffee Types

A survey was conducted in a city to understand coffee type preferences among residents from differen

Customer Satisfaction in a Retail Chain

A retail chain seeks to assess customer satisfaction. The chain is divided into 5 regions. Within ea

Designing a Double-Blind Experiment for a New Drug

A pharmaceutical company intends to test a new drug aimed at reducing blood pressure. To eliminate b

Effect of Diet on Cholesterol Levels

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

Effect of Population Variability on the Sampling Distribution

A simulation study is conducted drawing samples of size $$n = 30$$ from populations with the same me

Estimating Average Park Visit Duration

A study is conducted to assess the average length of time (in minutes) that visitors spend at a loca

Evaluating the Effectiveness of a New Drug

A clinical trial compared a new drug with a placebo regarding patient recovery. The data are summari

Firearm Safety Course Outcomes in Different Regions

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

Impact of a New Diet on Blood Pressure

A health clinic is investigating whether a new diet can reduce systolic blood pressure. Patients are

Impact of a Training Program on Employee Productivity

A company measured employee productivity before and after a new training program. Two independent sa

Investigating Data Variability in Statewide Math Test Scores

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

Physical Activity Levels by Region

A health study surveyed residents in different regions to assess their physical activity levels (cat

Prospective Cohort Study for Diabetes and Lifestyle Factors

A health organization plans to conduct a prospective cohort study to investigate how lifestyle facto

Sampling Distribution in Voter Polling

A polling organization is estimating the approval rating for a political candidate. Suppose the true

Scatterplot Analysis and Regression Line Interpretation

A researcher investigates the relationship between the number of hours studied (x) and exam scores (

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

Systematic Sampling in a Voter Preference Survey

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

Teaching Methods and Student Performance

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

Voting Preference Analysis

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

Water Quality and Fish Populations: Regression Analysis

An ecologist is studying the effect of water quality on fish populations in lakes. The regression an

Binomial Process in Quality Testing

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

BMI and Systolic Blood Pressure Regression Analysis

A study investigating the relationship between Body Mass Index (BMI) and systolic blood pressure (in

Coin Toss Experiment and Sample Size Effects

Consider an experiment where a fair coin is tossed repeatedly. Answer the following:

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

Daily Steps and Calorie Burn Regression Analysis

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

Dice Roll Sum Analysis

Two standard six-sided dice are rolled, and the sum $$X$$ of the numbers is recorded.

Effects of Noise Levels on Worker Productivity

A company is investigating whether ambient noise in the workplace affects employee productivity. Emp

Evaluating a Mobile App to Promote Healthy Eating

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

First Honest Encounter: Geometric Distribution

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

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: Encountering an Honest Person

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

Highway Construction Productivity Analysis

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

Hospital Stay Durations Analysis

A hospital collected data on the length of stay (in days) for patients following a particular surger

Insurance Sales Analysis

An insurance salesperson's daily sales for auto and home insurance are represented by two independen

Library Book Borrowing Times

A public library claims that the average time a book is borrowed is 3 weeks. A random sample of 40 b

Mobile App vs. Printed Pamphlet for Increasing Exercise Duration

A public health organization wants to determine whether a mobile app intervention or a printed pamph

Multistage Probability: Virus Infection on Campus Computers

On a university campus, 60% of computers run Windows, 30% run Apple, and 10% run Linux. A virus affe

Pharmaceutical Study: Recovery Time Distribution

A pharmaceutical study records recovery times (in days) for a treatment with the following distribut

Sampling Distribution of the Interquartile Range (IQR) via Simulation

A simulation is performed to calculate the interquartile range (IQR) for samples drawn from a non-no

Sampling Distribution of the Sample Range

Consider a simulation where samples are drawn from a uniform distribution on the interval $$[0,1]$$.

Simulated Binomial Sampling Distribution

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

Simulated Sampling Distribution of the Sample Variance

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

Simulating the Expected Value in a Lottery Game

Consider a lottery game with payouts given by the following probabilities: $$P(\$2)=0.5$$, $$P(\$5)=

Standardized Test Strategies and Scores

A standardized test administered to 800 students records the strategy used when unsure of an answer.

Student Testing Strategy and Scores Analysis

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

Urban Traffic Volume and Air Quality Regression Analysis

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

Website Conversion Rates: A/B Testing

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

Assessing Estimators for Baseball Weight

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

Assessing Estimators in Quality Testing

A factory uses different methods to estimate the maximum durable weight of a product. Five estimator

Battery Life Analysis Using Normal Distribution

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

Caffeine Content Analysis

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

Caffeine Content in Energy Drinks

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

Central Limit Theorem in Customer Service Times

In a call center, individual call durations are skewed with an average of $$\mu = 5$$ minutes and a

Coffee Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Pass Rates Between Two Schools

Two high schools are comparing their students' pass rates on a standardized test. School A had 200 s

Comparing Sampling Distribution of the Sample Mean in Normal vs. Skewed Populations

Two populations, A and B, both have the same mean $$\mu = 100$$ and standard deviation $$\sigma = 20

Comparing Variability in Two Measurement Methods

Two independent methods are used to measure the voltage of a battery. Method 1 produces individual m

Differences in Sample Means for Weight Loss Program

In a weight loss study, two groups are compared. Group A (n = 35) follows a new diet and has a sampl

Effect of Outliers on Sampling Distribution of the Mean

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

Effect of Sample Size on Variability

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

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

In a survey, it is found that 40% of respondents own a smartphone. A random sample of 200 respondent

Favorite Ice Cream Flavor Survey – Sampling Proportions

In a survey on ice cream preferences, past research indicates that approximately 40% of respondents

Graduation Rates by Gender

In a large school district, the graduation rate for girls is known to be 90%, while for boys it is 8

High Math Anxiety and Brain Activity

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

Lightbulb Life Expectancy Analysis

A particular brand of lightbulb has a lifespan that is approximately normally distributed with a mea

Lightbulb Lifespan Probabilities

A certain brand of lightbulbs has a lifespan that is normally distributed with mean $$\mu = 1500$$ h

Movie Theater Attendance by Genre Preference

A movie theater analyzed attendance frequency based on movie genre preference. The table below categ

Sample Size Calculation for Voter Support Estimation

A political survey aims to estimate the proportion of voters supporting a specific candidate with a

Sample Size Effects: Simulation Analysis

A simulation study is performed to examine the effect of sample size on the variability of the sampl

Sampling Distribution for Sample Proportions in Math Anxiety Study

A recent study estimates that 80% of people with high math anxiety experience brain activity similar

Simulated Sampling Distribution for Eco-Friendly Vehicle Mileage

An automobile manufacturer tests its eco-friendly vehicles whose fuel efficiency (in miles per gallo

Simulation of Sampling Distributions for Medians

A recent survey of high school students examined the number of hours studied per week. Although the

Stock Returns Probability Calculation

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

Survey on Learning App Preference

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

Technology Use and Academic Major

A survey was conducted to examine the relationship between academic major and technology usage frequ

Advertising Impact on Brand Recognition

A company runs a new advertisement in two regions. In Region 1, 210 out of 350 respondents recognize

Assessing Advertising Effectiveness with Proportion Data

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

Campaign's Voter Turnout Comparison

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

Checking Inference Conditions for Proportion Data

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

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

A study compared the effectiveness of two teaching methods. In a sample of 150 students taught by Me

Customer Satisfaction Survey by Region

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

Customer Satisfaction: In-Store vs. Online Shoppers

A retail store conducted a survey. Among in-store shoppers, 340 out of 400 reported being satisfied,

Designing a Survey for Voting Behavior

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

Evaluating a Policy Change via Proportion Hypothesis Testing

A city government wants to evaluate the impact of a new traffic safety policy. Before the policy, in

Evaluating Public Support for a Tax

A poll was conducted to measure public support for a proposed tax. In the first survey, 1000 voters

Investigative Analysis of Consumer Behavior

A company undertakes a comprehensive marketing research project to analyze consumer behavior towards

Manufacturing Process Comparison

A company employs two manufacturing processes. In Process A, a sample of 500 items produced 450 defe

Online Advertising Impact Study

An online retailer wishes to study whether exposure to a particular digital advertisement increases

Public Health: Smoking Rates by Region

A public health researcher wants to compare smoking rates between two regions. In Region 1, a survey

R&D Investment Success Rate

Two companies are comparing the success rates of their R&D investments. Company X had 100 projects w

Reading Program Impact Study

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

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

Smartphone Brand Preference by Income Level

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

Social Media Usage by Gender

A survey compares social media usage among different genders. In a sample of 400 males, 320 use soci

Sports Statistics: Free Throw Confidence Interval

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

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

Traffic Accident Analysis

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

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

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. Suburban Crime Reporting Rates

A survey was conducted to compare feelings of safety in urban and suburban areas. In an urban sample

Vaccine Hesitancy Survey Design

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

Voter Preference by Region

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

Voter Preference Comparison: Confidence Interval and Hypothesis Test

In a study of voter preferences, two independent samples were taken. In District A, a sample of 200

Advertising Budget and Sales Performance Analysis

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

Comparison of Pollutant Concentration in Two Rivers

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

Customer Satisfaction Survey

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

Diet Program Effectiveness

A research study was conducted to compare the effectiveness of two diet programs in achieving weight

Effect of a New Fertilizer on Crop Yield

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

Effectiveness of a New Drug on Pain Relief

A pharmaceutical trial tests a new drug intended to alleviate pain. In a double‐blind study, 40 pati

Election Polling Power Analysis

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

Impact of a Diet Program on Weight Loss

A weight loss study measures the weight of 20 participants before and after a 6‐week diet program. T

Life Span Analysis of Light Bulbs

A manufacturer claims that its light bulbs have a long lifespan. In a quality test of 15 randomly se

Machine Calibration Paired Data

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

Paired Data in Pre-Test and Post-Test Scores

A company runs a training program and measures employee performance before and after the program. Fo

Paired t-Test for Sleep Duration with Meditation Program

A study is conducted to evaluate the effect of a four-week meditation program on sleep duration. For

Physical Activity and Cholesterol Levels

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

Pre- and Post-Treatment Blood Pressure

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

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

Response Time in a Virtual Reality Task

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

Role of Random Sampling in Simulation Studies

A statistician conducts a simulation study by drawing 1000 random samples of size n = 25 from a data

Sample Size Effect on Component Length Confidence Interval

In a manufacturing process, the length of a component is measured. A sample of measurements yields a

Simulating the Effect of Sample Size on Confidence Interval Precision

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

Simulation of Sampling Distribution for Average Calorie Content in Energy Bars

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

Simulation of Sampling Distribution with Measurement Error

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

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

Training Program Performance Improvement

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

Voting Behavior and Political Affiliation

A study analyzes voting behavior among members of two political parties, Party A and Party B. The da

Academic Majors and Study Habits

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

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

Clinical Trial: Treatment Effects on Recovery Rates

In a clinical trial, patients are randomly assigned to one of three treatment strategies (Treatment

Customer Service Feedback in Retail Stores: Homogeneity Test

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

Dietary Preferences Among Age Groups: Chi-Square Test for Independence

Nutritionists surveyed 300 individuals to examine if dietary preference (Vegetarian, Non-Vegetarian)

Drug Efficacy Across Dosages

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

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

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

Examining Health Outcomes by Smoking Status

Researchers are interested in determining if there is an association between smoking status and heal

Extracurricular Participation and Academic Performance Independence Test

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

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 13: Customer Loyalty Across Store Branches

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

Gender and Preferred Social Media Platform

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

Genetic Trait Distribution Goodness-of-Fit

In a genetic cross the expected phenotypic ratio for a trait is 3:1 (dominant: recessive). A botanis

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

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

Goodness-of-Fit Test for Dice Fairness

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

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

Political Polling: Party Affiliation and Issue Stance

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

Production Line Defect Rates Homogeneity Test

A factory operates four production lines, each producing a sample of 200 items. The numbers of defec

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

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

Restaurant Choices Across Regions: Chi-Square Test for Independence

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

Service Provider Customer Satisfaction Homogeneity Test

Three service providers – Internet, Phone, and Cable – each surveyed 150 customers regarding their s

Student Course Preference and Major

A university surveys 300 students to determine if course delivery preference (Online vs. In-Person)

Type of Transportation and Commute Satisfaction

A survey of 530 commuters collected data on their primary mode of transportation (Car, Bus, Bike, Wa

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

Website Browser Market Share: Goodness-of-Fit Test

A tech website claims that the market share for internet browsers is as follows: Chrome 50%, Firefox

Advertising Budget and Store Revenue: Chain Comparison

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

Advertising Spend and Website Traffic

A company analyzed how its weekly advertising spend (in thousands of dollars) influences website tra

Car Age and Resale Value

A used car dealer is examining the relationship between a car's age (in years) and its resale value

Car Fuel Efficiency and Engine Size Comparison

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

Climate Change: CO2 Concentration vs Global Temperature Simulation

A climate scientist is exploring how atmospheric CO2 concentration (in ppm) relates to global averag

Coffee Consumption and Anxiety Levels

A psychologist investigates whether there is a relationship between the number of cups of coffee con

Comparing Slopes for Tutoring Effects on Test Score Improvement

A school district evaluates the effect of after-school tutoring on test score improvement for studen

Daily Study Hours and GPA

Researchers are interested in analyzing the relationship between the number of hours students study

E-Commerce Website Traffic and Sales

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

Effect of Study Habits on Exam Scores

Researchers are studying whether the number of extra study sessions (x) is related to improvement in

Effect of Study Intervention on Academic Performance

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

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 and Outdoor Temperature

A study on 30 households examined the relationship between outdoor temperature (x, in °F) and energy

Engine Temperature and Efficiency Loss

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

Hours of Sleep and Reaction Time

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

House Price Prediction Simulation

A real estate analyst is studying the relationship between house price (in $\$\,$ thousands) and squ

House Prices and Square Footage

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

Ice Cream Sales vs Temperature

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

Impact of Fertilizer Type on Plant Growth

A researcher is studying the effect of two different fertilizers on plant growth. The amount of fert

Impact of Study Hours on Exam Scores

A study examines the effect of weekly study hours ($$x$$) on exam scores ($$y$$) among 30 students.

Impact of Workout Hours on Body Fat Percentage

A fitness study collected data on the number of hours individuals work out per week (x) and their bo

Manufacturing Process Optimization

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

Medication Dosage vs Blood Pressure Reduction

A clinical researcher examined the effect of medication dosage (in mg) on blood pressure reduction (

Noise and Concentration Scores

Researchers are exploring the relationship between ambient noise (x, in decibels) in a study environ

Online Advertising Campaign and Web Traffic

A digital marketing team analyzed the relationship between advertising spending (in dollars) and the

Practice Time and Music Performance Skill

A study investigates the effect of weekly practice hours ($$x$$) on a music performance skill score

Predicting Sales Based on Advertising Budget

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

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

River Pollution Levels and Industrial Activity

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

Robotics and Efficiency

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

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

Temperature Effects on Motor Speed

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