AP Statistics FRQ Room

Application of the Empirical Rule to IQ Scores

Assume that IQ scores are normally distributed with a mean of $$100$$ and a standard deviation of $$

Boxplot Comparison: Stock Price Fluctuations Over Years

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

Cafeteria Food Satisfaction Proportion

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

Comparative Analysis using Stem Plot and Histogram

Two groups of students took a standardized test. Group A's scores have a five-number summary: minimu

Cumulative Frequency Graph Analysis for Age

A cumulative frequency graph is constructed for the ages of 100 individuals. The graph indicates the

Customer Ratings for Two Products

A market research firm collected customer ratings for two competing products. In a survey, 250 out o

Customer Satisfaction in Two Regions

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

Effect of a Multiplicative Transformation on Distance Data

A group of athletes has their running distances (in kilometers) recorded as: {5, 6, 8, 7, 10, 9}. Th

Effectiveness of a New Wearable Heart Rate Monitor

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

Event Attendance by Invitation Type

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

Favorite School Lunch Choices

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

Holiday Shopping Behavior: In-Store vs Online

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

Matching Data Sets and Estimating Percentiles

A cumulative frequency table for exam scores of 100 students is provided below: | Score | Cumulativ

Product Length Variability in Manufacturing

A manufacturing process produces items with lengths (in centimeters) distributed as shown in the fre

Restaurant Preference and Time Slot

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

School Year Length Preferences Survey

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

Shipping Delays at a Warehouse

At a large distribution center, shipping delays (in hours) are approximately normally distributed wi

Simulated Sampling Distribution of the Standard Deviation

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

Sleep Deprivation and Reaction Times

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

Stock Price Outlier Analysis

Consider the summarized daily stock prices (in dollars) of a company given by the following five-num

Stock Price Trends Through Parallel Boxplots

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

Student Major and Internship Status

A study of 200 college students recorded their major (STEM or Non-STEM) and internship status (Had I

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 Preferred Exercise Modalities

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

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,

University Lecture Attendance Analysis

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

Website Traffic: Click-Through Rate

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

Analyzing Curvilinear Relationship and Data Transformation

A botanist records the amount of fertilizer applied (x, in grams) and the resulting plant growth (y,

App Usage Trend: Free vs Premium Users

A tech company is studying how frequently users utilize a particular feature in their app. Two group

Bootstrap Simulation for the Regression Intercept's Sampling Distribution

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

Correlation vs. Causation Discussion

A study finds a high positive correlation between ice cream consumption and the number of drowning i

Customer Satisfaction: Online vs In-store Shopping

A retail company surveyed its customers about their satisfaction with online versus in-store shoppin

Dietary Effects on Blood Pressure

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

Email Marketing Response Rates

A company ran two email marketing campaigns and recorded the number of recipients who responded and

Evaluating Housing Market Trends Through Transformation

A real estate analyst studies the relationship between house square footage (x) and sale price (y, i

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

Exercise and Stress Investigation

A health research team collected data from 40 adults regarding their weekly exercise hours (quantita

Fitness Program Enrollment

A local gym evaluated enrollment trends by comparing two program types (Yoga vs. CrossFit) and atten

Impact of a New Study App on Academic Performance

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

Impact of Caffeine Intake on Reaction Time

In a laboratory study, researchers measured participants' reaction times (in seconds) after ingestin

Interpreting Calculator Output for Regression Analysis in Sports

A sports researcher investigates the relationship between players' height (in cm, X) and their free

Marketing Survey: Advertising Budget vs. New Customers

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

Pharmaceutical Dosage Testing

A pharmaceutical company produces tablets designed to contain an active ingredient with a prescribed

Predicting Apartment Rents

A real estate company collected data on apartment sizes (in square feet) and their monthly rents (in

Predicting Fitness Improvement from Exercise Duration

A fitness study examined the relationship between the daily exercise duration (x, in minutes) and th

Predicting Student Exam Scores from Study Hours

A researcher investigates the relationship between the number of hours a student studies (x) and the

Recovery Rates in Medical Treatments

A clinical trial was conducted to compare the recovery rates of patients using two different treatme

Recycling Attitudes Contingency Table Analysis

A survey of 200 community members was conducted to examine the relationship between recycling behavi

Residual Analysis in House Price Prediction

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

Restaurant Tip Analysis

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

Simulating the Sampling Distribution of the Sample Range in Bivariate Data

A researcher is interested in exploring the sampling distribution of the range of response variable

Simulation-Based Investigation of Chi-Square Distribution in Two-Way Tables

A researcher is interested in the chi-square test for independence in a two-way table. To understand

Specialty Coffee Orders at a Coffee Shop

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

Student Study Habits and GPA

A high school collects data from a random sample of 30 students to explore the relationship between

Study Hours and Exam Scores

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

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

Adverse Reaction Probability in a Drug Trial

In a clinical trial for a new drug, each patient has a 5% chance of an adverse reaction. In a sample

Cluster Sampling in Educational Research

A researcher wants to study academic performance across a large school district. The district is div

Comparing Retrospective and Prospective Studies in Outbreak Analysis

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

Comparison of Test Preparation Courses on SAT Scores

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

Customer Loyalty Programs: New vs. Established Store

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

Customer Satisfaction in a Retail Chain

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

Ebola Outbreak Study

A retrospective observational study during an Ebola outbreak in West Africa collected data on the nu

Effect of Diet on Cholesterol Levels

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

Effect of Noise Levels on Sleep Quality

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

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

Employee Job Satisfaction Survey

A company surveyed employees across three departments (Sales, HR, IT) regarding their job satisfacti

Hypergeometric Distribution in Quality Inspection

In a batch of 200 items, 10 are known to be defective. A quality inspector randomly selects 20 items

Impact of Advertising on Sales Revenue

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

Impact of Undercoverage Bias in Voter Surveys

A national polling organization uses a telephone directory to sample voters for an upcoming election

Implementing Simple Random Sampling

A researcher has a list of 500 registered voters and wants to conduct a survey about voter preferenc

Investigating Effects of Population Variability on Sampling Distributions

Two populations have the same mean $$\mu = 100$$ but different standard deviations: $$\sigma_1 = 10$

Investigating Voluntary Response Survey Bias

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

Online Ad Click-Through Rates and Sampling Distributions

An online advertising campaign has a click-through rate of 5%, and a webpage receives 500 visitors i

Physical Activity Levels by Region

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

Quality Control in Manufacturing

A manufacturing process produces items, each with a 2% chance of being defective. A quality control

Retrospective Study Analysis on a Health Outbreak

Epidemiologists are conducting a retrospective study on a past health outbreak by analyzing existing

Retrospective Study on Environmental Exposure and Health Outcomes

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

Simulation of the Sampling Distribution of the Sample Variance

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

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

Traffic Flow Analysis

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

Urban Green Spaces and Air Quality

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

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

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

Car Purchase Decisions by Region

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

Casino Chips: Sum and Variance Calculation

At a casino, couples receive free chips by drawing a card from two bags. One bag (X) contains the va

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

Coffee Shop Latte Prices

A national coffee shop chain wants to estimate the average price of lattes across its stores. A rand

Customer Satisfaction Survey

A retail company conducted a customer satisfaction survey both online and in-store. The results are

Drug Efficacy in Clinical Trial

A pharmaceutical company claims that at least 70% of patients will show improvement after receiving

Effects of Noise Levels on Worker Productivity

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

First Honest Encounter: Geometric Distribution

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

Fuel Efficiency Comparison between Two Vehicle Models

An automotive study compared the fuel efficiency of two car models. Model X was tested on 30 cars, y

Genetics: Inheritance Probabilities

In a certain plant species, each seed has a 75% probability of inheriting a dominant allele, indepen

Geometric Distribution: Encountering an Honest Man

In a certain ancient society, the probability that a randomly selected man is honest is $$0.12$$. As

Highway Construction Work Analysis

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

Highway Worker Productivity

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

Hospital Stay Durations Analysis

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

Impact of Advertising on Consumer Behavior

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

Impact of Sleep Duration on Reaction Time

A research lab is investigating how different amounts of sleep affect reaction times measured on a s

Insurance Policy Sales Analysis

An insurance salesperson is tracking her daily sales. For auto insurance, the number of policies sol

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

Manufacturing Quality Control for Defects

A factory produces electronic components, and historically the defect rate is expected to be less th

Online Advertisement Click-Through

A digital marketing campaign delivers 200 ad impressions, where each impression has a 3% chance of g

Online Shopping Behavior by Time of Visit

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

Quality Control Binomial Process

A manufacturing process produces items such that each item has a $$5\%$$ chance of being defective.

Raffle Ticket Payouts in a Fundraiser

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

Rare Defects and Poisson Approximation

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

Reading Preferences by Genre and Format

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

Restaurant Order Times

A fast-food restaurant records its order preparation times (in minutes) with the following distribut

Restaurant Orders by Meal Type and Tip Size

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

Simulating Clinical Trial Successes

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

Social Media Usage Patterns by Age Group

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

Startup Daily Profit Analysis

A startup estimates its daily profit with the following outcomes: a loss of $$200$$ dollars (probabi

Student Testing Strategy and Scores Analysis

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

Website Redesign and Sales Conversion Rates

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

Assessing Estimators in Quality Testing

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

Blood Pressure Reduction Study

A study examines whether a dietary supplement affects blood pressure. In the supplement group, the a

Coffee Bean Package Weight Analysis

A coffee company packages its coffee in bags. The weight of a coffee bag is normally distributed wit

Comparing Average Temperatures in Two Cities

City A has an average temperature of 70°F with a standard deviation of 5°F based on a sample of 50 d

Comparing Class Test Scores

Two independent classes took a standardized test. Class X (with $$n=30$$) had a mean score of 78 wit

Comparing Juice Bottling Process

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

Comparing Sampling Distributions from Two Populations

Population A has a mean of 100 with a standard deviation of 15, while Population B has a mean of 105

Difference in Sample Means: Genetic Mutations and Parental Age

Research indicates that 40-year-old men contribute an average of $$65$$ genetic mutations to their c

Difference in Sample Proportions: Revamped vs. Unrevamped Restaurant

A study compares customer behavior at two restaurants. At a revamped restaurant, 30% of a sample of

Dream Recall Simulation Study

A study on dream recall in college students found that the median number of dreams remembered per ni

Effect of Sample Size on Standard Error

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

Evaluating Genetic Mutations in New Fathers

A study examines the number of genetic mutations passed on by new fathers of different ages. It is e

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

Movie Theater Attendance by Genre Preference

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

Normal Approximation for Binomial Proportions

In a large survey, $$65\%$$ of respondents favor a new policy. In a random sample of $$100$$ respond

One-Sample vs. Two-Sample Sampling Distributions

A study is conducted to assess the effectiveness of a new teaching method. Two groups of 40 students

Regression Analysis and Inference in a Health Study

A health study investigates the relationship between Body Mass Index (BMI) and systolic blood pressu

Sampling Distribution of Differences in Proportions

In a study of customer eating habits at two fast‐food restaurants, it was observed that at Restauran

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

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

Social Media Engagement Proportions

A social media platform reports that 65% of its users engage with sponsored content. A random sample

Training Techniques and Marathon Finish Times

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

Using TI-84 for Z-Score Calculations in Sampling Distributions

A study on academic performance finds that student test scores are normally distributed with a mean

Analysis of Emergency Room Wait Times Satisfaction

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

Analyzing Election Poll Data: Estimating the Margin of Error

An election poll of 1000 voters produced a sample proportion of $$\hat{p}=0.48$$ for Candidate A. As

Analyzing Proportions as a Function of Batch Size

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

Comparing Two Dietary Supplements

A study compares two dietary supplements. In a sample of 200 consumers for Supplement A, 140 reporte

Confidence Interval for a Population Proportion

A public opinion poll designed to estimate the proportion of voters who support a new policy produce

Customer Satisfaction Survey by Region

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

Digital Platform Success Rate Comparison

Two schools use different digital learning platforms. In School X, 90 out of 150 students successful

Evaluating Public Support for a Tax

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

High School Extracurricular Participation

Two high schools are comparing the rates of extracurricular activity participation. In High School A

Hospital Safety Initiative Comparison

Two hospitals implement a safety initiative and then survey their nursing staff. In Hospital 1, 95 o

Marketing Campaign Response Rate Test

A marketing team asserts that their campaign increases customer engagement, expecting a response rat

Medical Study: Prevalence of a Risk Factor

A public health survey was conducted to determine the prevalence of a certain risk factor. In a simp

Power Analysis in Proportion Testing

A study is being designed to detect a 5% increase in the proportion of users who prefer a new app in

Public Survey on Recycling: Urban vs. Rural

A public survey investigated recycling habits in two different areas. In an urban area, 180 out of 3

Quality Control in Manufacturing

A manufacturing quality control team is checking the proportion of defective items in a production b

School Lunch Program Participation

A study examines participation in school lunch programs in two schools. In School X, 60 out of 150 s

Service Reliability Study Analysis

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

Social Media Usage Among Age Groups

A survey on social media usage was conducted among two age groups. Among individuals under 30, 160 o

Student Opinion on School Lunch Quality

A survey of 250 students at a high school found that 180 students reported that the school lunches a

Student Satisfaction in Two College Courses

A survey was conducted in two college courses to measure student satisfaction. In Course 1, 90 out o

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

University Policy Support Analysis

A university claims that 60% of its students support a proposed policy change. A random sample of 20

Vaccine Hesitancy Survey Design

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

Web Advertisement Click-Through Rates

An online marketing team is comparing the click-through rates of two advertisements. Ad A was shown

Advertising Spending and Sales Regression Analysis

A researcher investigates the relationship between advertising spending (in thousands of dollars) an

Air Conditioning Energy Consumption

A manufacturer claims that its new air conditioning unit uses on average 6.5 kilowatts of electricit

Coffee Consumption and Alertness Analysis

The scatterplot below depicts data on the number of cups of coffee consumed per day (x-axis) and an

Coffee Consumption and Alertness Scores

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

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

Customer Preference on Smartphone Features

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

Daily Energy Consumption Analysis: Hypothesis Test

A consumer agency is investigating a claim that a new brand of air-conditioning units uses only $$6.

Diet Choice and Energy Levels

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

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

Drug Effectiveness on Blood Pressure

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

Education and Annual Income Analysis

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

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

Effect of Training on Typing Speed: Paired Analysis

A company implemented an intensive typing training program. Typing speeds (in words per minute) were

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

Evaluating a Sleep Intervention

A fitness center implements a sleep intervention program aimed at increasing the average number of h

Exam Score Analysis with Unequal Sample Sizes

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

Examining Teaching Methods

A school is comparing two teaching methods: Traditional and Modern. Student outcomes are classified

Machine Downtime Analysis

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

Pre- and Post-Treatment Blood Pressure

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

Precision in a Manufacturing Process

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

Quality Control in Production

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

Simulating Sampling Distribution of the Sample Range

A quality control analyst in a factory runs a simulation study by drawing 1000 samples of size n = 1

Simulation of the Sampling Distribution for Mean Salary

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

Study Hours and GPA Analysis

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

Academic Majors and Study Habits

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

Age Group and Exercise Habits

A fitness survey categorizes participants into three age groups (Teen, Adult, Senior) and records th

Branch Service Quality

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

Candy Flavor Preferences: Goodness-of-Fit Test

A local candy shop claims that customer preferences for its four candy flavors (chocolate, strawberr

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 1: Distribution of Customer Preference for a New Snack

A snack company claims that the preferences for flavors of its new snack follow the proportions: Fla

FRQ 2: Association Between Smoking Behavior and Gender

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

FRQ 9: Student Enrollment Preferences Across Tracks

A high school offers four different tracks: STEM, Humanities, Arts, and Vocational. The school expec

FRQ 11: Distribution of Emergency Calls by Time of Day

A city’s fire department expects that emergency call volumes vary by time of day according to histor

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

Goodness-of-Fit Test in Marketing Campaign Response

A company’s marketing campaign is expected to yield customer reactions in five groups with the follo

Independence Test: Dietary Supplements and Energy Levels

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

Job Satisfaction Among Departments: A Homogeneity Test

A company sampled employees from four departments (A, B, C, D) to record job satisfaction. The data

Learning Style and Major Association Independence Test

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

Library Membership and Age

A library survey examines whether there is an association between age group and type of membership (

Preferred Payment Methods: Chi-Square Test for Homogeneity

A market research firm conducted surveys in three different cities regarding preferred payment metho

Public Opinion on Policy: Chi-Square Test for Independence

A poll surveyed 600 individuals regarding their stance (Support or Oppose) on a new public policy, a

Public Transportation and Demographics: Chi-Square Test for Independence

City planners conducted a survey of 300 residents to determine if the preferred mode of transportati

Restaurant Menu Distribution Analysis

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

Restaurant Popularity Goodness-of-Fit

A local food festival features four types of cuisines: Italian, Chinese, Indian, and Mexican. Organi

Simulating the Distribution of the Chi-Square Statistic

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

Social Media Platform Usage

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

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

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

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

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

Testing a Fair Die – Chi-Square Goodness-of-Fit

To determine if a six-sided die is fair, a student rolls it 600 times. Under the assumption of a fai

Traffic Accident Severity

In a study of traffic accidents on a highway, the outcomes were classified as Minor, Major, or Fatal

Voter Turnout by Age Group: Test for Independence

A survey reports voter turnout among four age groups: 18-29, 30-44, 45-64, and 65+. The two variable

Advertising Budget and Sales Revenue

A marketing analyst is studying the relationship between a company’s monthly advertising budget (in

Agricultural Yield and Fertilizer Simulation

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

Altitude vs Cooking Time

A culinary scientist is investigating whether altitude affects cooking time for a specific recipe. D

Crop Yield and Fertilizer Application

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

Customer Satisfaction and Wait Times

A restaurant chain surveyed 50 customers to study the effect of wait time (x, in minutes) on satisfa

Daily Study Hours and GPA

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

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 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

Engine Size and Fuel Efficiency

An automotive engineer is interested in the relationship between engine displacement (in liters) and

Fertilizer Effect on Plant Growth: Experimental Design

An agricultural study aims to assess the effect of different levels of fertilizer on plant growth. R

Height and Weight Relationship: Male vs Female

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

Ice Cream Sales and Temperature

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

Ice Cream Sales vs Temperature

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

Impact of Teaching Methods on Math Performance

A school district is interested in determining whether a new teaching method improves performance on

Internet Speed and Streaming Buffer Time

A technology company studies the relationship between home internet speed (x, in Mbps) and streaming

Marketing Impact: Social Media Activity vs. Product Sales

A company collected data from 45 markets to investigate the effect of social media advertising hours

Measurement Error Impact on Slope Estimation: Simulation Study

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

Medical Dosage and Blood Pressure Reduction

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

Medication Dosage and Blood Pressure Reduction

A hospital study evaluated the effect of increasing medication dosage on blood pressure reduction. T

Medication Dosage and Recovery Time

A clinical trial explores the impact of a new drug's dosage (measured in mg) on recovery time (measu

Modeling Blood Pressure Response to Medication Dosage

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

Noise and Concentration Scores

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

Rainfall and Crop Yield

An agricultural study investigates the relationship between total rainfall (in inches) during the gr

Relationship Between Hours Studied and Test Scores

A study collects data from 30 students on the number of hours spent studying (x, in hours) and their

Relationship Between Stress Level and Reaction Time

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

Social Media Influence on Product Sales Simulation

A business analyst wants to understand the effect of time spent on social media advertising (in hour

Sports Performance: Practice Time vs Shooting Accuracy

A basketball coach investigates how weekly practice hours affect shooting accuracy percentages among

Sports Performance: Training Hours and 100m Dash Times

For 20 professional athletes, a regression analysis was performed to predict 100m dash time (y, in s

Stock Price and Market Index: Simulation of Slope Distribution

An economist is investigating the relationship between the daily returns of an individual stock and

Temperature Effect on Ice Cream Sales

An ice cream vendor recorded daily temperature (in °F) and daily ice cream sales (in dollars) over 3

Wind Speed vs Power Output

An energy analyst is exploring the effect of wind speed (in m/s) on the power output (in kilowatts)