AP Statistics FRQ Room

AP Course Enrollment Among High School Seniors

A survey of 2200 high school seniors collected data on the number of AP classes they are taking. The

College Admissions Test Scores

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

College Graduation Rate Analysis

A college claims its graduation rate is 85%. In a survey of 200 students, 162 of them graduated with

Comparing Cumulative Frequency Graphs for Age Distributions

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

Comparing Sleep Hours: High School vs College

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

Cumulative Frequency Curves: Comparing 1860 and 1980 U.S. Populations

Cumulative frequency curves for the U.S. population in 1860 and 1980 are provided. For 1860, half th

Error Rates in Two Production Machines

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

Evaluating Marketing Strategies: Online Ad A/B Test

A company performed an A/B test for two versions of an online advertisement to compare their click-t

Examining Data Variability in Sports Statistics

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

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,

Hypothesis Testing: Reaction Time vs Age

In an experimental study on reaction times (in milliseconds) versus age (in years), the following re

Impact of Incentives on Survey Participation

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

Internet Usage Among College Students

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

Investigative Task: Public Park Usage Study

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

Job Satisfaction Across Departments

A company administered job satisfaction surveys in two different departments. In Department 1, 120 o

Movie Theater Attendance

Ticket sales at a movie theater are assumed to be normally distributed with a mean of $$150$$ seats

Relative Frequency Calculation from Pet Ownership Survey

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

Sampling Distribution and Confidence Interval Implications for Household Incomes

A sociologist is studying household incomes, which are right-skewed. The sociologist uses a simulati

School Year Length Preference Survey Analysis

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

Shopping Satisfaction: Online vs. In-Store

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

Simulated Sampling Distribution of the Range from a Uniform Distribution

Consider a population with a uniform distribution on the interval [0, 1]. A simulation is performed

Simulation of Sampling Distribution of a Proportion in a Medical Recovery Study

In a clinical trial, suppose the true proportion of patients who recover from a treatment is 0.80. A

Sports Performance: Basketball Free Throws

A basketball player makes free throws with a success probability of 75%. In a game, she attempts 20

Stem-and-Leaf Analysis of Ages

A stem-and-leaf plot displays the ages (in years) of participants in a study as follows: 2 | 1 3 5

Study Program Effectiveness Hypothesis Test

A researcher wants to determine if a new study program increases test scores. In a random sample of

Treatment Outcomes in Hospital Study

A hospital conducted a study on two treatments (Treatment X and Treatment Y) to evaluate patient out

Analysis of Influential Points in Athlete Performance Data

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

City Bicycle Usage Study

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

College Major by Gender

A study was conducted at a college to examine the relationship between major category and gender. St

Comparing Regression Lines With and Without an Influential Point

A company collected data on its monthly sales (Y, in millions of dollars) and advertising spending (

Constructing a Contingency Table from Raw Data

A researcher surveying 100 individuals collected the following raw counts regarding gender (Male, Fe

Correlation between Exercise and Weight Loss

A fitness center collects data on the number of hours clients exercise per week and the weight loss

Environmental Study: Air Pollution vs. Respiratory Issues

A public health researcher collects data from 50 cities to examine the relationship between air poll

Evaluating Coefficient of Determination in Athletic Performance

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

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

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

Impact of a New Study App on Academic Performance

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

Marketing Survey: Advertising Budget vs. New Customers

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

Online Course Engagement and Performance

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

Online Learning Preferences

A survey was conducted among 200 students to determine their preferences for online learning. Studen

Online Ratings and Restaurant Revenue

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

Retail Store: Age and Spending Patterns

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

Reverse Regression: Predicting Hours Worked from Earnings

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

Sampling Distribution of the Sample Range and Its Limitations via Simulation

A statistician is interested in exploring the sampling distribution of the sample range from a bivar

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

Smartphone Brand Loyalty

A market survey examined customer satisfaction across three smartphone brands (Brand X, Brand Y, and

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 Preference Survey

A school conducted a survey to determine students' favorite extracurricular clubs, recording two cat

Study Habits and Exam Pass Rates

A researcher compared exam pass rates between two groups of students enrolled in different study pro

Study Habits and Exam Scores: Regression Inference

A study of 30 students collects data on hours studied (x) and exam score (y). The regression analysi

Training Hours and Error Rates in Manufacturing

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

Warehouse Shipping Times

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

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

Analysis of Recycling Behavior

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

Analysis of Smoking Habits Among Adults

A public health researcher surveyed adults and categorized them by age group (Young, Middle, Senior)

Analyzing a Charity Fundraising Event

A charity event recorded donations categorized by size (Small, Medium, Large) and by donor type (Fir

Analyzing Bias in Convenience Sampling at a Mall

A researcher conducts a convenience survey at a local shopping mall to gauge consumer satisfaction w

Analyzing Store Price Data

A retail chain claims that the average price of a particular product is at most \($10\). To test thi

Assessing Nonresponse Bias in Telephone Surveys

During a telephone survey on community health, only 40% of the contacted individuals respond. Answer

Assessing Sampling Techniques in Market Research for a New Product

A company plans to gauge consumer preferences for a new product by sampling shoppers at a busy mall

Cluster Sampling in a University Study on Student Satisfaction

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

Comparing Sampling Variability Across Methods

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

Customer Loyalty Programs: New vs. Established Store

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

Effects of Diet Programs on Weight Loss

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

Environmental Study on Pollution Levels

A retrospective study examined water quality from 40 rivers in a region, measuring the concentration

Evaluating Bias in a Sampling Process: Voluntary Survey

A city council conducts a voluntary online survey regarding community safety. Out of 150 responses,

Evaluating the Effectiveness of a New Drug

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

Flu Vaccination Campaign and Illness Spread

A hospital is reviewing its flu vaccination campaign by comparing the incidence of flu among vaccina

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

Investigating Data Variability in Statewide Math Test Scores

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

Observational Study on Dietary Habits and Exam Performance

A high school is interested in studying the relationship between students' dietary habits and their

Observational Study Versus Experiment in Healthcare

A hospital wants to study the impact of a new dietary program on diabetic patients’ blood glucose le

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

Online Tutoring and Student Performance

A school district implements an online tutoring program aimed at improving student math performance.

Participation in Extracurricular Activities

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

Prospective Cohort Study for Diabetes and Lifestyle Factors

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

Public Health Intervention on Smoking Cessation

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

Simulation Study on the Distribution of the Sample Range

A researcher is studying the spread of values in a uniformly distributed population on the interval

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

Systematic Sampling for a School Survey on Sports Participation

A high school with 500 students wants to survey opinions about sports participation. The principal d

Traffic Flow System and Commuting Times

A city is testing a new traffic flow system designed to reduce commuting times during rush hour. The

Voting Preference Analysis

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

Basketball Free Throw Analysis: Binomial and Transformation

A basketball player has a free throw success rate of $$0.75$$ and takes $$16$$ free throws in a game

Comparing Consumer Spending at Two Malls

Two shopping malls record the average spending per visitor. Mall A has a sample of 100 visitors with

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

Comparing Sampling Distributions Under Different Population Variabilities

A simulation is run for two populations: Population A has a low variance and Population B has a high

Defects from Two Machines

A factory has two machines producing gadgets. Machine A produces 100 gadgets per hour with a defect

Energy Consumption Random Variables

In a small town, the daily household energy consumption (in kWh) is modeled by the following distrib

Evaluating a New Teaching Technique in High School

A school district is testing a new interactive teaching technique against the traditional method. Ce

Exam Score Cumulative Distribution

The following table displays the distribution of scores on an exam from 200 students:

Geometric Distribution: Encountering an Honest Person

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

High School SAT Scores Analysis

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

Household Income and Entertainment Expenditure Regression Analysis

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

Influence of Diet on Blood Pressure

A nutritionist is investigating how different dietary plans—specifically, low-carb, Mediterranean, a

Manufacturing Process Downtime

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

Movie Rating Analysis on Streaming Platforms

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

Quality Control Binomial Process

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

Restaurant Order Times

A fast-food restaurant records its order preparation times (in minutes) 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

Stock Market Daily Returns

A particular stock’s daily percentage return is modeled by a discrete random variable with the follo

Student Majors and Graduation Outcome

A university tracked graduation outcomes for 300 students by major. The summarized data is provided

Tip Amounts from Different Meal Services

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

Website Session Duration Analysis

A tech company is analyzing website usage and wants to estimate the typical duration of user session

Blood Pressure Reduction Study

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

Bootstrapping and the Sampling Distribution of the Mean

A researcher collects daily sales data from a small store over 30 days. The observed sample mean is

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 Durability of Lightbulbs

A study was conducted to compare the longevity of light bulbs manufactured by two different factorie

Comparing School Test Scores

School A has a test score distribution with a mean of 75 and a standard deviation of 8, and School B

Constructing a 95% Confidence Interval for Battery Lifetime

A quality control study tests the lifetimes of batteries. A random sample of 50 batteries has a samp

Consumer Reviews: Variability Analysis

A popular online product has consumer ratings on a 1-to-5 star scale. In a random sample of 100 revi

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

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

Estimator Evaluation in Baseball Manufacturing

In a quality control study for manufacturing professional baseballs (true mean weight = $$146$$ gram

Evaluating Bias in Strength Estimation

A manufacturing process for components uses a new estimator to measure average component strength. A

Evaluating Biased and Unbiased Estimators

A quality control manager is evaluating five different estimators (labeled A through E) for estimati

Evaluating Manufacturing Estimators

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

Evaluation of Estimators in Baseball Manufacturing

A sports equipment manufacturer is evaluating five different estimators (A, B, C, D, and E) used to

LED Lightbulb Lifespan Probability Analysis

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

Manufacturing Process Consistency and Variability

A manufacturer recently implemented a new process intended to reduce variability in product weights.

Music Streaming Service Satisfaction

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

Sampling Distribution for Differences in Sample Proportions in Political Polling

In a political poll, two districts are surveyed. In District A, 60% of 500 voters support a policy,

Sampling Distribution for Differences in Sample Proportions: Political Polls

An exit poll surveys two candidates. Candidate X receives support of 48% from a sample of 400 voters

Smartphone Battery Life Comparison

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

Student Extra-Curricular Participation

A school conducted a survey to understand students' involvement in extracurricular clubs. The table

Student Test Scores Sampling Distribution

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

Using invNorm in Sampling Distributions: Statistical Thresholds

Scores on a standardized test are normally distributed with a mean of $$\mu = 500$$ and a standard d

Website Load Time Evaluation

A popular website has load times that are approximately normally distributed with a mean of 3.5 seco

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 Voter Turnout Using Confidence Intervals

An exit poll of 800 voters revealed that 560 voted in favor of Candidate Y. Construct a 95% confiden

Assessing Website Conversion Rate

A company claims that its website has a conversion rate of 5%. To test this claim, a random sample o

Checking Inference Conditions for Proportion Data

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

College Acceptance Rate Comparison

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

Community Recycling Program Study

A city implements a program aimed at increasing household recycling rates. Two neighborhoods with si

Comparing Hospital Readmission Rates

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

Comparing Two Dietary Supplements

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

Comprehensive Analysis of Confidence and Significance in Survey Data

A political researcher conducted a two-part survey to analyze voter opinions on a new policy. The fi

Customer Satisfaction Survey – Comparing Two Stores

A retail company conducted a customer satisfaction survey at two different store locations. At Store

Diet Choices by Gender

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

Effectiveness of a Public Health Intervention: Investigative Task

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

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

Medical Treatment Outcomes

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

One-Sided Election Polling Analysis

In a survey of 600 likely voters, 330 support a particular candidate. The candidate’s campaign claim

Online Education Satisfaction

A study comparing satisfaction with education methods surveyed two groups. One group of online stude

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

Public Opinion on Policy Change

A survey is conducted on a new tax policy. In a simple random sample of 500 voters, 260 indicated th

Reading Program Impact Study

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

Satisfaction with Mobile App Features

A tech firm surveys 650 mobile app users and finds that 390 users are satisfied with the app feature

Smoking Cessation Campaign Study

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

Social Media Usage and Political Opinions

A survey explored the relationship between political leaning (Liberal vs. Conservative) and whether

Sports Participation by Gender and Sport Type

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

University Policy Support Analysis

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

Urban vs. Suburban Crime Reporting Rates

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

Voter Turnout Behavior Survey

A political organization implements a get-out-the-vote campaign in several precincts and wishes to d

Web Conversion Rate Analysis

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

Battery Life Study

A battery manufacturer claims that the new battery model has an average lifespan of $$\mu$$ hours. A

Clinical Drug Trial: Comprehensive Data Analysis

A clinical trial is conducted to compare the effect of a new drug versus a placebo in lowering chole

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

Computer Downtime Analysis

A sales representative suspects that his company's computers have higher average non-operational (do

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

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

Experience and Salary Analysis

The scatterplot below represents data on employees' years of experience (x-axis) and their annual sa

Fertilizer Impact on Plant Growth

An agricultural researcher investigates whether a new fertilizer affects plant growth. Two independe

Lifespan of New Light Bulbs

A company tests the lifespan of a new type of light bulb. A random sample of 18 bulbs shows a mean l

Manufacturing Measurement Variability

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

Mean Gas Mileage Confidence Interval

A car manufacturer wants to estimate the true mean gas mileage of a new model. A random sample of 12

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

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

Quality Control: Machine Calibration

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

Response Time in a Virtual Reality Task

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

Simulating 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 from a Bimodal Population

A researcher is studying a population that exhibits a bimodal distribution (e.g., test scores from t

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 for Mean Rainfall Amounts

A meteorologist simulates the sampling distribution of the average daily rainfall (in inches) record

Simulation of Sampling Distribution in a Clinical Trial

A medical researcher conducts a simulation to analyze the sampling distribution of the mean systolic

Simulation of the Sampling Distribution for Mean Salary

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

Social Media Usage Before and After an Intervention

A researcher studies the effect of a digital detox program on daily hours spent on social media. For

Study of Daily Traffic Flow

A transportation engineer studies the flow of traffic on a busy freeway. Data collected over 50 rand

Voting Behavior and Political Affiliation

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

Yearly Comparison of Mathematics Test Scores

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

Clothing Preference and Gender: Test for Independence

A clothing store surveyed customers to see if there is an association between gender (male, female)

Customer Satisfaction Across Regions

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

Diet and Exercise Frequency: Independence Test

A health study of 240 participants recorded data on diet quality (Healthy, Unhealthy) and exercise f

Diet Preferences Among Teenagers: Goodness-of-Fit Test

A survey of 150 teenagers categorizes their diet preferences as Vegetarian, Vegan, Omnivore, and Pes

Distribution of Types of Crimes in a City

A study compares the types of crimes in two districts of a city. District A reported: Property = 80,

Drug Efficacy Across Regions: Homogeneity Test

A pharmaceutical company tests the effectiveness of a new drug in four regions. Each region conducts

Examining Political Ideology: Chi-Square Test for Homogeneity

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

Exercise Frequency and Music Preference – Chi-Square Test for Independence

A gym surveyed 150 members to study the relationship between exercise frequency (categorized as Low,

FRQ 16: Association Between Marital Status and Voting Behavior

A study examines whether marital status is associated with voting behavior for Party X versus Party

Fruit Distribution Goodness-of-Fit Test

A fruit vendor claims that the distribution of fruits in a basket follows the percentages: 40% Apple

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

Job Satisfaction Among Departments: A Homogeneity Test

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

Manufacturing Defect Distribution Goodness-of-Fit

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

Music Genre Preferences Across Cities – Chi-Square Test for Homogeneity

A market research firm surveyed residents in four different cities (City A, City B, City C, City D)

Observations of Wildlife Distribution

A wildlife biologist expects that four bird species in a habitat occur in equal proportions. In a su

Phone Usage and Preferred App: Chi-Square Test for Independence

A tech survey collected data on 250 smartphone users on two categorical variables: phone operating s

Product Packaging Preference Across Regions

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

Product Preference Independence Test by Gender

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

Race Participation in Marathon

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

Smoking and Exercise Frequency Independence Test

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

Social Media Platform Usage

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

Social Media Platform Usage and Age: Test for Independence

A survey of 400 individuals collects data on their most-used social media platform (Platform A, Plat

Sporting Event Results: Homogeneity Test

A study investigates whether the win distribution among five tournament teams differs. Each team's r

Test for Independence: Political Opinions on Climate Change

A survey of 400 registered voters categorized by party affiliation (Democrats, Republicans, Independ

Traffic Accident Severity

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

Transportation Mode Among City Residents

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

Vehicle Type Distribution Goodness-of-Fit Test

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

Voter Preferences Across Regions: Homogeneity Test

A political analyst surveys 100 voters from each of three regions (North, South, Midwest) regarding

Advertising Reach and Customer Acquisition

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

Agricultural Study: Fertilizer and Crop Yield

In an agricultural study involving 52 plots, researchers investigated the effect of fertilizer usage

Altitude vs Cooking Time

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

Biking Speed and Heart Rate

A sports scientist is investigating the relationship between average biking speed (in mph) during ex

Car Mileage and Tire Pressure

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

Coffee Consumption and Alertness

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

Dosage of Medication and Blood Pressure Reduction

A clinical researcher investigates whether the dosage of a new medication (in mg) is associated with

Effectiveness of a New Drug on Blood Pressure

A pharmaceutical company is investigating whether a new drug reduces blood pressure as the dosage (i

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

Engine Size vs Highway Fuel Efficiency

An automobile researcher is studying the relationship between engine size (in liters) and highway fu

Engine Temperature and Efficiency Loss

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

Exercise and Cholesterol Reduction

A health study investigated the effect of weekly exercise hours (x) on cholesterol reduction (y, in

Exercise Duration and Heart Rate Recovery

A fitness researcher examines the effect of exercise duration (in minutes) on heart rate recovery ti

Housing Price Estimation

A real estate analyst examines the relationship between the age of a house (in years) and its price

Industrial Emissions and Air Quality

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

Interpreting Confidence Intervals from Multiple Studies

Two independent studies estimate the slope of a regression line that relates coffee consumption to p

Medical Dosage and Blood Pressure Response

A clinical trial tests the impact of a new medication dosage ($$x$$, in mg) on blood pressure reduct

Medication Dosage vs Blood Pressure Reduction

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

Mobile App Usage Study

A study examines the relationship between time spent on a mobile app (in minutes) and user satisfact

Online Course Hours and Final Grades

An educational researcher is modeling final course grades (y, in percentage) as a function of the nu

Predicting Blood Pressure Based on Age

A health study collected data on systolic blood pressure (in mm Hg) and age (in years) for 40 adults

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

River Pollution Levels and Industrial Activity

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

Social Media Influence on Product Sales Simulation

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

Social Media Use and Sleep Quality

A study investigates the relationship between daily hours spent on social media (x) and nightly slee

Student Performance and Study Hours

Researchers examine the relationship between hours studied (x) and exam scores (y). The regression a

Study Hours and SAT Scores: Private vs Public

A researcher studied the relationship between study hours (x) and SAT scores (y) among students from

Technology Training and Productivity

A technology company wants to know if the number of training hours (x) influences employee productiv

Temperature and Ice Cream Truck Sales

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

Traffic Flow Analysis: Regression Slope Simulation

A transportation planner is analyzing the relationship between the number of vehicles on a roadway a

Vehicle Weight and Fuel Efficiency

A study investigates the relationship between vehicle weight (in pounds) and fuel efficiency (in mil