AP Statistics FRQ Room

Almond Packet Weight Confidence Interval

A quality control team at an almond packaging company wants to estimate the mean weight of its packe

Analysis of Weather Data: Daily Rainfall

A meteorologist recorded daily rainfall (in mm) over a month and summarized the data in the followin

Analyzing Z-Scores and Normal Distribution

Assume that a particular set of data is normally distributed with a mean of 100 and a standard devia

Analyzing z-Scores from a Frequency Distribution

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

Boxplot Comparison: Stock Price Fluctuations Over Years

A company's daily stock prices over five consecutive years are summarized in the following table: |

College Admissions Test Scores

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

College vs. High School Sleep Study

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

Daily Caloric Intake Data Analysis

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

Effect of Constant Adjustments on Mean Salary

Consider the salaries (in dollars) of six employees given below: $3,000; $7,000; $15,000; $22,000; $

Effects of Adding a Constant on Measures of Spread

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

Holiday Shopping Behavior: In-Store vs Online

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

Impact of Transformations on Data

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

Investigative Task: Public Park Usage Study

A city park department seeks to understand how weather conditions affect park attendance. They plan

Machine Adjustment Methods in Manufacturing

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

Meditation Training for Stress Reduction

A psychological study is designed to determine if meditation training reduces stress levels among co

Nature Exposure and Mood Improvement

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

NBA Wins: Analyzing Back-to-Back Stem Plots

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

Regression Analysis: Blood Sugar and Calorie Intake

Researchers are studying the relationship between daily calorie intake and blood sugar levels measur

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

Simulation of Taxi Annual Mileage Sampling Distribution

A researcher is investigating the annual mileage driven by taxi cabs in a metropolitan area. The pop

Sleep Deprivation and Reaction Times

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

Social Media Campaign Effectiveness on Engagement

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

Social Media Platform Usage by Gender

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

Unit Conversion Impact on Summary Statistics

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

University Course Selection by Gender

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

Advertising Campaign and Sales Analysis

A company tracked the number of social media impressions (in thousands, x) and corresponding product

Analyzing a Survey on Social Media Use and Sleep

A researcher surveys 100 college students to study the relationship between the number of hours spen

Art Exposure and Creativity Scores

A survey of 40 art students collected data on the number of hours per week they attend art exhibits

Coffee Shop Drink Preference

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

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

Diet Program Success Rates

A nutritionist compared the effectiveness of two diet programs by surveying participants on whether

E-Commerce Site Traffic and Revenue Analysis

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

Effect of Advertisement Frequency on Brand Recognition

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

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

Evaluating Sales Team Performance

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

Free Throw Performance in Basketball

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

Online Ratings and Restaurant Revenue

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

Political Polling: Approval Ratings

A polling organization is studying the approval ratings of a political leader among urban and rural

Public Health Campaign on Smoking Cessation

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

Retail Store: Age and Spending Patterns

A retail chain studied the spending patterns of 50 customers. The summary statistics are: mean age =

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 Comparison of Unstandardized vs. Standardized Regression Coefficients

A data analyst performs a simulation study to compare the sampling distributions of unstandardized a

Simulation of the Mean Residuals in a Regression Model

In a regression analysis, residuals (the differences between observed and predicted values) are expe

Startup Revenue Growth

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

Student Study Habits Survey

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

Urban Noise and Sleep Quality Study

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

Voter Turnout by Gender

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

Warehouse Shipping Times

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

Website A/B Testing for Click-Through Rates

A technology company is testing two versions of its website (Version A and Version B) to see which o

Willingness to Adopt Electric Vehicles

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

Workforce Diversity Study

A corporation conducted a study to analyze the distribution of employees across different job levels

Analysis of Recycling Behavior

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

Bootstrapping the Sampling Distribution of a Mean

A researcher has collected exam scores from 15 students and wishes to estimate the sampling distribu

Cluster Sampling in a University Study on Student Satisfaction

A university administration wants to gauge overall student satisfaction with campus life. The survey

Comparative Simulation of the Mean and Median Sampling Distributions

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

Comparing Sampling Variability Across Methods

A study to estimate the mean age of teachers uses four different sampling methods. Ten samples are t

Customer Satisfaction Proportion Sampling

A company has found that 80% of its customers are satisfied with its service. A survey is conducted

Differences in Data Collection Techniques: Face-to-Face vs. Online Surveys

A political research firm collects survey data about voter opinions through both face-to-face interv

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

Efficacy of a Mobile App for Tracking Physical Activity

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

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 a New Teaching Method

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

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

Exercise Frequency and Cholesterol Levels

A study investigates the relationship between the number of hours of exercise per week (x) and total

Experimental Design: Evaluating a Review Course for SAT Scores

A study aims to evaluate whether a new SAT review course improves student scores. Students are rando

Impact of Advertising on Sales Revenue

A chain of retail stores seeks to understand the relationship between advertising expenditures (in $

Interpreting Observational Study Data on Exercise and Blood Pressure

A study tracks daily exercise minutes and resulting changes in blood pressure for 100 adults over a

Manufacturing Processes and Product Lifespan

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

Physical Activity Levels by Region

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

Predicting Blood Pressure from Age: Regression and Inference

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

Predicting Car Mileage from Engine Size

A study of 80 cars investigates the relationship between engine size (in liters, x) and fuel efficie

Randomized Block Design in Evaluating a Teaching Method

A school district is conducting an experiment to compare a new teaching method with the traditional

Randomized Controlled Trial: Vaccine Efficacy

A clinical trial is conducted to evaluate a vaccine. 200 subjects receive the vaccine and 200 receiv

Replication in Experimental Designs: Water Purification Study

Researchers are testing various water purification techniques in an experimental study. Replication

Retrospective Versus Prospective Public Health Studies

A public health agency is planning to study the spread of a novel pathogen. They have access to exte

Sampling Distribution in Voter Polling

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

Sampling Variability in Teacher Performance Evaluations

A school district collects teacher performance evaluations through student surveys. The administrati

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

Smartphone Usage and Sleep Quality

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

Social Media Usage and Mental Health

Researchers are studying the impact of social media usage on mental health among teenagers. A survey

Stratified Sampling in an Educational Survey

A school district consists of three types of schools: elementary (40%), middle (30%), and high schoo

Survey on Public Opinion Regarding Public Transit

A survey of 200 city residents was conducted to assess support for an increase in public transit fun

Teaching Methods and Student Performance

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

Voter Behavior: Support for Policy X Among Different Age Groups

A political survey measured support for Policy X among two age groups. In a sample of 150 young vote

Work-from-Home vs. In-Office Job Satisfaction

A human resources study surveyed job satisfaction among employees working from home and those workin

Assessing the Impact of a New Advertisement Campaign

A retail company wants to measure the effect of a new advertisement campaign on store sales. A sampl

Coffee Consumption and Alertness Level Regression Analysis

A study examines the influence of coffee consumption (number of cups per day) on an individual's ale

Comparing Customer Satisfaction in Two Coffee Shops

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

Comparing Daily Sales between Two Store Locations

Two retail stores report their average daily sales. Store 1 has a sample size of 40, with a mean dai

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

Engine Size and Fuel Efficiency Regression Analysis

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

Highway Construction Productivity Analysis

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

Impact of Advertising on Consumer Behavior

A marketing firm investigated the effect of advertisement exposure on purchasing decisions. The foll

Impact of Study Aid on Exam Pass Rates

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

Insurance Sales Analysis

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

Online Shopping Behavior by Time of Visit

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

Political Polling: Voting Intentions by Age Group

A polling agency surveyed 300 voters about their intention to vote 'Yes' or 'No' on a particular iss

Public Opinion Survey on Local Issues

A political analyst is conducting a survey to gauge public opinion on various local government polic

Reading Preferences by Genre and Format

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

Sales Calls Geometric Distribution

A salesperson makes calls until she gets her first sale. The probability of getting a sale on any gi

Sampling Distribution of the Sample Mean from a Normal Population

A simulation experiment draws repeated random samples from a normally distributed population with $$

Sampling Distribution of the Sample Range

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

Scatterplot Regression Analysis on Study Habits

A researcher collects data on the number of hours students study (x) and their exam scores (y). The

Simulated Sampling Distribution for a Binomial Variable with Larger n

A simulation is executed where 50 independent Bernoulli trials with probability $$p = 0.4$$ are perf

Simulated Sampling Distribution of Survey Proportions

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

Simulating Clinical Trial Successes

A new drug has a success probability of 0.65. In a clinical trial, 30 patients are treated independe

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)=

TV Advertising and Product Demand Regression Analysis

A company analyzes the relationship between TV advertising spending (in thousand dollars) and produc

Website Redesign and Sales Conversion Rates

A company tested its website performance before and after a redesign. The old design resulted in 90

Website Server Demand Modeling

Historical data for a website shows that the daily number of server requests (in thousands) follows

Bacterial Count in Water Samples

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

Consumer Preferences for Soft Drinks

A market research firm collected data on consumer satisfaction for three soft drink brands. The tabl

Effect of Outliers on Sampling Distributions

A data set of 50 observations is known to have a mean of $$100$$ and a standard deviation of $$15$$.

Effect of Sample Size on Sampling Variability

A company monitors customer wait times at a service center. The standard deviation for an individual

Employee Training Program Evaluation

A company evaluated the effectiveness of its training programs by mode of delivery (Online vs. In-Pe

Energy Drink Caffeine Analysis

An energy drink contains on average $$200$$ mg of caffeine with a standard deviation of $$10$$ mg. A

Environmental Study: Tree Heights

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

Estimator Bias: Maximum vs. Mean in Soccer Scores

A soccer coach considers using the maximum number of goals scored in a series of 10 games as an esti

Evaluating Estimators for Baseball Weight

A quality control department is evaluating five different statistical estimators to measure the weig

Financial Returns: Biased vs. Unbiased Estimators

Investment analysts use two estimators to predict the expected return of a financial asset. Estimato

Hospital Emergency Room Waiting Times

The waiting times (in minutes) for patients in a busy hospital emergency room are approximately norm

LED Lightbulb Lifespan Probability Analysis

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

Music Streaming Service Satisfaction

A music streaming service is comparing satisfaction levels between Free and Premium subscription use

Sampling Distribution of the Maximum: Weather Temperature Extremes

A climatologist is studying daily maximum temperatures in a city. The theoretical population maximum

Simulated Sampling Distribution for Eco-Friendly Vehicle Mileage

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

Simulating the Sampling Distribution of the Range

A researcher is interested in the range of scores on a standardized test. The population range is kn

Survey on Preferred Beverage

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

Advertising Impact on Brand Recognition

A company launched an advertising campaign in two regions. In Region 1, a post-campaign survey of 50

Air Quality Health Survey Design

A public health department is conducting a survey to estimate the proportion of residents suffering

Analysis of Emergency Room Wait Times Satisfaction

A hospital surveyed patients about their satisfaction with emergency room wait times. In a sample of

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

College Acceptance Rate Comparison

Two high schools wish to compare college acceptance rates. School X admitted 75% of its applicants o

Comparing Hospital Readmission Rates

Two hospitals report their 30-day readmission rates. Hospital A had 60 readmissions out of 200 patie

Diet Choices by Gender

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

Environmental Policy Opinion Poll

A survey was conducted to assess public support for a new environmental policy. In an urban area (Gr

Estimating Customer Satisfaction

A local coffee shop surveyed 200 customers to assess their satisfaction. Out of the 200 customers, 1

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

Factory Quality Control Analysis

In a factory, quality control is carried out by inspecting a sample of items. Out of 800 items inspe

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

Measuring Customer Preferences

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

Medical Treatment Outcomes

A clinical trial compares the outcome of a new drug with a placebo. Patients were classified as eith

Online Shopping Proportion Analysis

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

Physical Activity App Study

A startup company developed a new mobile application aimed at encouraging physical activity. Users a

Planning a Comparative Survey

A researcher intends to conduct a survey comparing two groups and wants to detect a minimum differen

Political Polling: Estimating Voter Support

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

Public Health: Smoking Rates by Region

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

Research on Smoking Cessation Program

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

Retail Store Customer Satisfaction Confidence Interval

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

Service Reliability Study Analysis

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

Smartphone Brand Preference by Income Level

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

Smoking Cessation Campaign Study

A public health campaign aims to reduce smoking rates. A survey is then conducted to estimate the pr

Social Media Campaign Engagement Analysis

A company runs a social media campaign aiming for a target engagement rate of 40%. In a sample of 60

Social Media Usage by Gender

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

STEM Club Gender Representation Study

A high school is investigating the proportion of female members participating in its STEM clubs. Par

Student Housing and Meal Plan

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

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

Voter Preferences by Age Group

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

Web Conversion Rate Analysis

A company is analyzing its website conversion rates over two consecutive months. In Month 1, 90 conv

Website A/B Testing

An online retailer is testing two versions of its webpage (Version A and Version B) to determine whi

Battery Life Analysis for a Smartphone Model

A manufacturer claims that its new smartphone model has an average battery life of at least $$9.5$$

Comparing 3-Point Percentage Rates

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

Comparing Average Wait Times at Two Coffee Chains

A study is conducted to compare customer wait times at two coffee shop franchises. The following sum

Comparing Two Diet Programs on Weight Loss

A nutritionist wants to compare two different diet programs to determine which one leads to greater

Comparing Two Diets

A nutritionist compares the effects of two diets on weight loss. In a study, Diet 1 (n = 30) results

Difference in Mean Cholesterol Drop between Diet Plans

A nutritional study compares two diet plans. For Diet A, a sample of 50 participants shows an averag

Education and Annual Income Analysis

The scatterplot below represents data on years of education (x-axis) and annual income in dollars (y

Evaluating a Mobile App's Impact on Daily Step Count

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

Exercise and Resting Heart Rate Analysis

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

Fuel Efficiency of Hybrid Cars

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

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

Investigative Analysis of Customer Service Performance Metrics

A company collects data on customer service performance across two centers. For a focused study on c

Machine Cycle Time Analysis

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

Machine Downtime Analysis

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

Manufacturing Process Improvement

A manufacturing company implements a new process intended to reduce component production times. For

Math Test Scores and Teaching Methods

A school district is comparing the effectiveness of two teaching methods on math test scores. Two in

Medical Test Accuracy and Diagnosis

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

Monthly Sales Performance Analysis

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

Pre-Test and Post-Test Scores Analysis

The scatterplot below represents data on students' pre-test scores (x-axis) and post-test scores (y-

Precision in a Manufacturing Process

A company claims that the mean diameter of a manufactured part is $$10$$ mm. An independent quality

Study Hours and Test Scores Regression Analysis

The scatterplot below displays data on college students' study hours (x-axis) and their correspondin

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

Weight Loss Confidence Interval

A nutritionist is studying the effectiveness of a new weight loss program. A random sample of 20 par

Academic Majors and Study Habits

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

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

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

Chi-Square Analysis of Traffic Light Phases

A transportation engineer hypothesizes that the timing of traffic light phases (green, yellow, red)

Consumer Preference for Advertisement Types

A company believes that consumer preference for advertisement type follows the distribution: Online

Customer Complaint Categories – Chi-Square Goodness-of-Fit

A customer service center categorizes complaints into four types: Billing, Technical, Service, and O

Customer Product Color Preference Analysis

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

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

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

Die Fairness: Goodness-of-Fit Test

A six-sided die was rolled 120 times with the following observed frequencies: Face 1: 10, Face 2: 20

Employee Training Program: Comparing Certifications Across Departments

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

Examining Health Outcomes by Smoking Status

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

FRQ 2: Association Between Smoking Behavior and Gender

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

FRQ 3: Voter Preferences by Age Group: A Homogeneity Test

A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup

FRQ 12: Employee Training Program and Job Promotion

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

Genetic Ratios in Plant Breeding – Chi-Square Goodness-of-Fit

In a plant breeding experiment, a dominant-recessive trait is expected to follow a 3:1 phenotypic ra

Goodness-of-Fit for Beverage Preferences

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

Independence Test: Dietary Supplements and Energy Levels

A fitness center surveyed 250 members about their use of dietary supplements (Yes/No) and their self

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

Pet Ownership in College Residences

A study investigates whether there is an association between college residence type and pet ownershi

Quality Control in Manufacturing

A factory produces items that are classified into three quality classes: Class I, II, and III. The p

Race Participation in Marathon

A marathon organizer expects the racial participation to follow these percentages: Group 1 = 30%, Gr

Restaurant Menu Distribution Analysis

A popular restaurant chain claims that the distribution of orders among four cuisine types (Italian,

Robustness of Chi-Square Test: Small Expected Counts

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

Simulated Chi-Square Distribution for Voting Patterns

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

Simulated Data: Random Number Generator Uniformity Test

A random number generator produced 1000 numbers that were binned into 10 equal intervals. The observ

Smoking and Exercise Frequency Independence Test

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

Sports Preferences by Gender: Chi-Square Test for Independence

A survey of 300 students recorded their preferred sport (Basketball, Soccer, Tennis) and their gende

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

Traffic Light Malfunction Analysis

A city’s transportation department monitors traffic light performance. They expect that 90% of signa

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

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

Vehicle Type Distribution Goodness-of-Fit Test

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

Voting Behavior and Demographics

A survey collected responses from 700 voters regarding their political affiliation (Democrat, Republ

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

Workplace Safety Compliance

A company records the safety compliance of employees in two departments: Manufacturing and Administr

Advertising and Sales Revenue Regression Analysis

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

Advertising Data: Predicting Sales

A company wants to study how advertising spending (x, in thousands of dollars) affects product sales

Agricultural Yield and Fertilizer Simulation

An agricultural scientist is examining the relationship between the amount of fertilizer used (in po

Altitude and Cooking Time

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

Assessing Environmental Pollution Impact

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

Biomarker Levels and Disease Severity Simulation

A biomedical study examines the relationship between blood biomarker levels (in mg/dL) and disease s

Coffee Consumption and Alertness

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

Education Research: Impact of Class Size on Performance Simulation

An education researcher is investigating the impact of class size on average student test scores. A

Elevation and Atmospheric Pressure

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

Employee Performance from Experience

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

Energy Consumption and Temperature: Simulation Study

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

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

Exercise Duration vs Heart Rate

A fitness researcher analyzed the relationship between exercise duration (in minutes) and heart rate

Exercise Time and Weight Loss

A personal trainer examines whether the number of hours exercised per week is related to weight loss

Fish Population and Pollution Levels

Biologists are studying whether increased pollution levels (x, in parts per million) are associated

Marketing Campaign Effectiveness Simulation

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

Plant Growth vs Fertilizer Amount

An agronomist is studying the effect of fertilizer amount (in kg/ha) on plant growth (in cm) in a co

Predicting Ice Cream Sales from Temperature

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

Relationship Between Exercise Time and Cholesterol

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

Relationship Between Study Hours and Exam Scores

A school counselor is investigating the relationship between the number of hours a student studies a

Retail Store Foot Traffic and Sales Revenue

A retail chain is studying the relationship between daily foot traffic (number of people) and daily

River Pollution Levels and Industrial Activity

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

Sleep Hours and Reaction Time

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

Social Media Engagement and Online Sales

An e-commerce company investigates the relationship between daily social media engagement (measured

Social Media Usage vs GPA

A researcher analyzed the relationship between weekly hours spent on social media and college GPA us

Temperature and Electricity Consumption

A power company studies the relationship between daily average temperature (in °C) and electricity c

Temperature and Electricity Usage

A utility company is studying the relationship between the average outside temperature (in °F) and t

Temperature and Ice Cream Truck Sales

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

Tree Growth Analysis: Simulated Slope Distribution

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