AP Statistics FRQ Room

Analyzing Cumulative Frequency and Percentiles from Exam Scores

The cumulative frequency table below summarizes the scores on an exam for a class of 100 students:

Boxplot Comparison: Stock Price Fluctuations Over Years

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

Comparing Sleep Hours: High School vs College

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

Dietary Preferences by Gender

A survey collected responses from 270 individuals regarding their dietary preference (Vegetarian, No

Effectiveness of a New Wearable Heart Rate Monitor

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

Effects of Multiplicative Transformations on Test Scores

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

Effects of Sample Size on the Sampling Distribution in Temperature Data

A meteorologist is studying daily high temperatures in a city over the summer. The temperatures are

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

Favorite School Lunch Choices

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

Home Run Distances Analysis

Consider the following set of home run distances (in feet) measured at 13 ballparks: $$\{387, 400,

Impact of Outliers on Measures of Center

Two datasets represent the annual household incomes (in thousands of dollars) in two similar neighbo

Leadership Training and Employee Satisfaction

A business management study is investigating whether participation in a leadership training workshop

Lottery Ticket Analysis

The probability of winning on a single lottery ticket is $$0.001$$. A person buys tickets one after

Medication Efficacy in Reducing Blood Pressure

A research team is designing an experiment to evaluate the efficacy of a new preventative medication

NBA Team Wins: Distribution Assessment

The numbers of wins for NBA teams in two conferences are summarized using comparative data displays.

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

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 Survey on Categorical Preferences

A high school conducted a survey of 400 students regarding their preferred school day length. The re

Simulated Sampling Distribution of the Standard Deviation

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

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

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

Sports Performance: Basketball Free Throws

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

Stock Price Outlier Analysis

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

Subway Train Arrival Times

Subway wait times are normally distributed with a mean of $$5$$ minutes and a standard deviation of

Test Scores Histogram Interpretation

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

Z-Scores and Percentile Ranks in a Test Examination

Assume that the scores on a standardized test are normally distributed with a mean of $$80$$ and a s

Analyzing Temperature Effects on Electricity Consumption

A utility company collected data on average daily temperature (in °F) and electricity consumption (i

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

Comparing Two Online Learning Platforms

An education technology firm wants to compare two online learning platforms to determine which one l

Constructing a Scatterplot from Given Data

The following table lists paired observations of variables x and y. | x | y | |----|----| | 5 |

Constructing and Interpreting Prediction and Confidence Intervals

A study performs a linear regression analysis to predict exam scores (y) based on the number of prac

Correlation and Coefficient of Determination in Exam Performance

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

Customer Satisfaction Survey

A retail store surveyed customers regarding their visit frequency (Frequent vs. Infrequent) and over

Customer Satisfaction: Online vs In-store Shopping

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

Elderly Health Program Evaluation

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

Exercise and Stress Investigation

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

Exploring Temperature and Ice Cream Sales

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

Fitness Tracker Analysis

A fitness center collected data from individuals using fitness trackers, recording daily steps (x) a

Housing Prices and Square Footage Analysis

A real estate analyst collected data on various houses regarding their square footage (in square fee

Impact of Sample Size on the Sampling Distribution of the Sample Mean in Two-Variable Data

A dataset containing paired observations of hours of exercise (x) and minutes of sleep (y) is used i

Impact of Skewness on the Sampling Distribution of the Sample Mean in Bivariate Data

A researcher collects data on household income (x) and spending on luxury goods (y), noting that inc

Medical Test Accuracy and Disease Prevalence

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

Museum Visits and Visitor Satisfaction

A local museum surveyed 40 visitors about the number of times they visited the museum in the past ye

Quality Control in Manufacturing

A factory produces light bulbs and historically 5% of bulbs are defective. A quality control inspect

Recovery Rates in Medical Treatments

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

Residual Plot Analysis for a Blood Pressure Study

A medical study uses a regression model to predict blood pressure (Y) from sodium intake (X). The re

Simulation of the Impact of Measurement Error on the Sampling Distribution of Pearson's r

A study measures the relationship between two variables, but with varying degrees of measurement err

Social Media Engagement Analysis

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

Social Media Engagement Study

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

Study Habits and Exam Pass Rates

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

Tech Company Productivity Analysis

A tech company collected data on the number of programming hours (x) and the number of bugs fixed (y

Voting Behavior and Media Consumption

A political analyst surveyed 300 individuals to study the relationship between media consumption and

Wait Time and Meal Satisfaction

A restaurant collected data from 40 customers on their wait time (in minutes) and meal satisfaction

Workforce Diversity Study

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

Bootstrapping the Sampling Distribution of a Mean

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

Central Limit Theorem and Coffee Consumption

In a certain region, the average daily coffee consumption is 3 cups with a standard deviation of 1 c

Customer Feedback for a New Product

A technology company collected customer feedback regarding a new product via two purchasing channels

Diet, Weight Loss, and Regression Analysis

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

Effect of Sleep Duration on Reaction Time

In an experimental study on college students, the relationship between sleep duration (in hours, x)

Effectiveness of a Training Program on Certification Outcomes

In a study evaluating a certification training program, 80 employees who attended the training had 6

Estimating Average Park Visit Duration

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

Evaluating Bias in a Sampling Process: Voluntary Survey

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

Flu Vaccination Campaign and Illness Spread

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

Impact of Advertising on Product Purchase

A company conducted a study on the effect of different advertisement types (Online, TV, Print) on pr

Investigating Response Time in Emergency Calls

A retrospective study collected data on the response times (in minutes) of emergency services from 6

Mobile App User Engagement

A mobile app company uses a simple random sample of 100 users to estimate the average daily usage ti

Observational Study Versus Experiment in Healthcare

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

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Social Media Use and Academic Performance

A study is conducted to explore the relationship between daily hours spent on social media (x) and a

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

Voting Patterns in a Retrospective Study

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

AP Exam Score Distribution: Cumulative Probability Analysis

The table below shows the percentage of students achieving each AP exam score for a given year.

Applying Chebyshev's Inequality in Quality Control

A production process yields items with an average weight of 50 grams and a standard deviation of 5 g

Basic Probability Rules in Testing Strategies

A standardized test uses different strategies when a student is uncertain about an answer. The table

Binomial Distribution in Lightbulb Defectiveness

In a quality control test, the probability that a lightbulb is defective is $$0.1$$. Answer the foll

Campus Computer Virus Spread: Multistage Probability Calculation

On a university campus, computers run on three different operating systems: Windows (60%), Apple (30

Coffee Shop Latte Prices

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

Coin Flip Game Strategies

In a game show, contestants face two different coin flip challenges. In Challenge A, you win if the

Comparing Average Test Scores of Two Teaching Methods

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

Comparing Consumer Spending at Two Malls

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

Comparing Simulation Results for Rainy Days

A simulation study recorded weather in two cities over a 30-day month. The results are as follows:

Cumulative Distribution Function Analysis for Daily Customers

A small store tracks its daily customer counts and summarizes the data with the following cumulative

Customer Retention and Marketing Strategies

A company tested two marketing strategies to improve customer retention. Strategy 1 retained 240 out

Daily Steps and Calorie Burn Regression Analysis

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

Diet Preferences and Health Outcome

A nutrition study surveyed 200 individuals regarding their diet and health outcome. The data are sum

Employee Training and Department Performance

A company recorded the outcomes of a recent employee training program across three departments. The

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

Game of Score Sums

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

Highway Construction: Expected Daily Miles

A highway construction project operates under varying weather conditions. On a clear day, workers la

Insurance Policy Sales Analysis

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

Investment Returns: Sum and Difference of Random Variables

An investor has two independent investments with the following annual return distributions: Investm

Multi-center Clinical Trial for a New Vaccine

A large-scale clinical trial is conducted across several hospitals to evaluate the efficacy of a new

Quality Control in Manufacturing

A factory produces items with a defect probability of $$0.05$$ per item. Items are produced in batch

Rare Defects and Poisson Approximation

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

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

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

Simulated Distribution of Sample Proportions with a Biased Coin

A simulation uses a biased coin with a probability of heads $$p = 0.8$$. In each simulation run, the

Simulated Sampling Distribution of Survey Proportions

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

Simulation in Hypothesis Testing: Generating a Reference Distribution

A researcher employs simulation to generate the sampling distribution of a test statistic under the

Software Use in Organizations

A survey of 230 organizations recorded the primary operating system used in different departments. T

Standardized Test Strategies and Scores

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

University Admissions Multistage Process

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

Urban Traffic Volume and Air Quality

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

Weather Temperature and Ice Cream Sales Regression Analysis

A vendor investigates the relationship between daily temperature (in °F) and ice cream sales (in dol

Analysis of Athletic Performance Improvements

A coach is comparing the performance improvements of athletes following two different training progr

Assessing Estimators for Baseball Weight

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

Assessing Estimators in Quality Testing

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

Biased and Unbiased Estimators in Quality Control

A company uses three estimators (A, B, C) to estimate the average weight of its packaged product. Th

Biased Estimator in Quality Control

A manufacturer uses an estimator to measure the maximum strength of a new material. A simulation of

Blood Pressure Reduction Study

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

College Major and Internship Experience

A university conducted a survey on students' internship experiences across different majors. The tab

Comparing Biased Estimators via Simulation Outcomes

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

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

Confidence Interval and Sampling Distribution in Height Estimation

A researcher aims to estimate the average height of college students with a margin of error of $$1$$

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 Proportions: Fast Food Restaurant Study

A study compares customer behavior at two fast-food restaurants. At the revamped restaurant, $$25\%$

Effect of Outliers on Sampling Distribution of the Mean

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

Effect of Sample Size on Variability

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

Emergency Room Wait Times Analysis

In a hospital, emergency room wait times are approximately normally distributed with a mean of 30 mi

Employee Training Program Evaluation

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

Environmental Study: Tree Heights

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

Estimating Average Commute Time

A study suggests that the average commute time in a metropolitan area is $$\mu = 30$$ minutes with a

Examining Bias in Sample Maximums

In a quality control study, an analyst records the maximum defect size from samples of 10 items take

Exploring the Sampling Distribution of a Proportion in Smartphone Ownership

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

Genetic Mutations in New Fathers

It is estimated that 40-year-old men contribute on average $$65$$ genetic mutations to their offspri

Hospital Emergency Room Waiting Times

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

Manufacturing Process Consistency and Variability

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

Normal Approximation for Binomial Proportions

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

Political Opinion Poll on Policy Support

A political opinion poll was conducted to determine the relationship between political affiliation a

Quality Control in Baseball Production

A sports manufacturing company uses five different estimators (A, B, C, D, and E) to estimate the we

Regional Customer Satisfaction Analysis

A marketing study examines customer satisfaction in two regions. In Region A, the true satisfaction

Sampling Distribution of a Sample Proportion for Disease

In a health study, it is known that 5% of the population has a particular disease. A random sample o

Simulated Sampling Distribution of Sample Medians

A survey of 500 high school students collects data on the number of dreams remembered per night—a va

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 and Empirical Distribution: Study Habits

A researcher collects data on weekly study hours for high school students. In an initial sample of 1

Social Media Engagement Proportions

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

Social Media Usage by Age Group

A survey examined the social media usage intensity among different age groups. The table below categ

Survey on Policy Support in Two Regions

A survey was conducted in two regions regarding support for a new public policy. In Region A, out of

Training Techniques and Marathon Finish Times

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

Air Quality Health Survey Design

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

Assessing the Fairness of a Die

A six-sided die is rolled 600 times to test for fairness. In these 600 rolls, the result "6" appears

Comparing Participation Rates in Exercise Programs Across Cities

Two cities conducted surveys about participation in exercise programs. City X had 250 participants o

Comparing Two Proportions: Online vs. In-Store Shopping Preferences

A researcher compares shopping preferences. In a sample of 300 online shoppers, 210 prefer online sh

Comparing Voter Turnout between Two Regions

Two regions conducted independent surveys before an election. In Region A, a random sample of 200 vo

Customer Loyalty Program Impact Study

A retail company introduces a new loyalty program and compares the proportion of customers making re

Diet Preference in Age Groups

A study compares the proportion of individuals following a vegan diet between two age groups. Among

Effectiveness of a Drug

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

Effectiveness of a Social Media Campaign

A company launched a social media campaign to increase brand engagement. Two surveys were conducted:

Gender Differences in Product Preference

A market survey was conducted to measure interest in a new gadget. A sample of 400 males showed that

Gender Representation in STEM Fields

A study was conducted to compare gender representation in STEM fields among recent graduates. In a s

Government Policy Approval Confidence Interval

A polling organization surveyed 800 voters to measure the approval of a recent government policy. Am

Hospital Infection Rates: Hypothesis Testing

A hospital claims that its post-surgery infection rate is 2%. In a sample of 500 patients, 18 develo

Interpreting a Confidence Interval for Hybrid Learning Preference

At a high school, a survey of 100 students reveals that 40 prefer a hybrid learning model.

Marketing Strategies: Hypothesis Testing for Two Proportions

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

Measuring Customer Preferences

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

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

Physical Activity App Study

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

Political Campaign Support Analysis

A political campaign conducted a survey to determine support for a candidate. In the survey, a simpl

Product Defect Rates in Manufacturing

A manufacturing plant operates two production lines. Line A produced 1000 items with a defect rate o

Public Health: Influenza Vaccination Rates

A public health study compares influenza vaccination rates between urban and rural areas. In urban a

Reading Program Impact Study

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

Sample Size Determination for Desired Margin of Error

A researcher wishes to estimate the proportion of households that recycle with a margin of error of

Social Media Influence Study

A marketing firm is investigating whether exposure to a popular social media influencer affects the

Sports Statistics: Free Throw Confidence Interval

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

Urban vs. Rural: Survey on Public Transportation Usage

A survey was conducted to compare the use of public transportation between urban and rural residents

Advertising Budget and Sales Performance Analysis

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

Advertising Spend and Website Traffic Analysis

The scatterplot below presents data on monthly advertising spending (in thousands of dollars, x-axis

Assessing a New Teaching Method

A study compares two teaching methods to assess their impact on student performance. In a randomized

Clinical Trial on Blood Pressure Reduction

A clinical trial is conducted to compare the effectiveness of two medications in reducing blood pres

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

Customer Satisfaction at Two Store Branches

A retail chain collects customer satisfaction ratings (on a scale of 1 to 10) from two store branche

Customer Satisfaction Survey

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

Customer Wait Time in Service

A supermarket manager records the wait times (in minutes) for customers at a checkout counter. In a

Daily Energy Consumption Analysis: Hypothesis Test

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

Determining Sample Size for a Cholesterol Study

A researcher aims to estimate the mean cholesterol level in a population with a margin of error of 2

Diet Program Effectiveness

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

Dosage Effect on Symptom Reduction

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

Effectiveness of an Online Learning Platform

An online learning platform claims that students using it achieve an average course score of at leas

Employee Productivity Analysis

A study compares employee productivity scores between two departments. Department 1 (n = 30) has a s

Engine Emissions Compliance

An environmental agency is monitoring engine emissions to ensure compliance with regulations that re

Exercise and Resting Heart Rate Analysis

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

Impact of a Study Program on Exam Performance

A school introduces an intensive study program and measures students' exam scores before and after i

Impact of a Study Technique on SAT Scores

A high school implements a new study technique intended to improve student SAT scores. A group of 40

Light Bulb Lifespan Hypothesis Test

A company advertises that its light bulbs have an average lifespan of 1200 hours. A quality control

Paired t-Test for Sleep Duration with Meditation Program

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

Power Analysis in a Drug Efficacy Study

A pharmaceutical company is testing a new drug intended to lower blood pressure. The test is a one-s

Pre- and Post-Treatment Blood Pressure Analysis

In a clinical trial, patients' systolic blood pressure is measured before and after a new treatment.

Production Efficiency Comparison Across Shifts

A factory compares production times between two work shifts. Shift A has a sample mean production ti

Recovery Rates in Two Hospitals

A study compares recovery rates between two hospitals. Patients are classified as 'Recovered' or 'No

Sample Size Effect on Component Length Confidence Interval

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

Screen Time and Eye Strain Analysis

The scatterplot below depicts data on daily screen time (in hours, x-axis) and reported eye strain 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 with Measurement Error

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

Sodium Intake and Systolic Blood Pressure Analysis

The scatterplot below shows data on individuals' daily sodium intake (in mg, x-axis) and their systo

Study Hours and Test Scores Regression Analysis

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

Training Hours and Employee Productivity Analysis

The scatterplot below shows data on training hours (x-axis) and employee productivity, measured in u

Age Group and Exercise Habits

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

Association between Exercise Frequency and Diet Type

A survey of 200 college students examines whether there is an association between exercise frequency

Bacteria Types in Environmental Sampling: Goodness-of-Fit Test

An environmental scientist collects 180 bacterial samples from a river and categorizes them into fou

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

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

Demographic Trends in Streaming Service Preferences

A streaming service study examines if the preferences among four platforms (Netflix, Hulu, Amazon, D

Diet Preference Among Athletes

In a study, three groups of athletes (Football, Basketball, Soccer) were surveyed regarding their di

DNA Mutation Distribution – Chi-Square Goodness-of-Fit

A geneticist hypothesizes that the distribution of DNA mutations in a sample of 300 cells is as foll

Drinking Habits and Health Outcomes: Test for Independence

A health study surveys 300 individuals, recording their drinking habits (Never, Occasionally, Regula

Drug Efficacy Across Dosages

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

Examining Political Ideology: Chi-Square Test for Homogeneity

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

FRQ 9: Student Enrollment Preferences Across Tracks

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

FRQ 10: Impact of Marketing Strategy on Product Sales

A company implements a new marketing strategy and wants to determine if the acceptance rate of its p

Game Outcome Distribution

A board game produces three outcomes: win, loss, and draw. The expected probabilities for these outc

Gender and Preferred Social Media Platform

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

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

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

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

Homogeneity in Student Class Preferences

Three high schools conducted surveys to determine whether student preferences for online versus in-p

Job Satisfaction Among Departments: A Homogeneity Test

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

Market Analysis: Brand Preference

A market analysis firm surveyed 200 consumers to determine their preference among three competing br

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)

Online Shopping Preference by Age Group

A survey of 330 consumers examines the preference for online shopping platforms among different age

Participation in Extracurricular Activities: Chi-Square Test for Homogeneity

A school district wants to compare participation rates in extracurricular activities among high scho

Pet Ownership and Residence Type Independence Test

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

Quality Control: Defective Items in Production Lines

A factory operates 4 production lines. It is believed that the proportion of defective items is the

Smoking and Exercise Frequency Independence Test

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

Socioeconomic Status and Book Reading Frequency: Independence Test

A survey of 600 individuals collects data on their socioeconomic status (Low, Medium, High) and book

Test for Independence: Political Opinions on Climate Change

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

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

Coffee Consumption and Alertness

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

Coffee Consumption and Alertness Score

A nutrition study collected data on the number of cups of coffee consumed per day (x) and an alertne

Coffee Consumption and Anxiety Levels

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

Coffee Temperature vs Reaction Time

A study was conducted to examine the effect of coffee temperature (in $$^\circ C$$) on reaction time

Crop Yields and Fertilizer Usage

Agricultural researchers are investigating the effect of fertilizer amount (in kg per hectare) on cr

Customer Satisfaction and Wait Times

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

Dosage-Response in Drug Trials Simulation

A clinical researcher investigates the effect of drug dosage (in mg) on patient response scores. To

Electricity Usage and Temperature

An energy analyst examines how average daily temperature (x, in °F) affects household electricity us

Engine Size and Emissions

An environmental engineer is studying the relationship between engine size (in liters) and vehicle e

Engine Size vs Highway Fuel Efficiency

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

Exercise Frequency and Resting Heart Rate

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

Exercise Time and Weight Loss

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

Hours of Sleep and Reaction Time

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

House Prices and Square Footage

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

Housing Prices Prediction

A real-estate analyst investigates how the selling price of houses relates to their size (in square

Influence of Advertising Budget on Sales

A firm is investigating the effect of its advertising budget (in thousands of dollars) on weekly sal

Medical Dosage and Blood Pressure Response

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

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

Study Program Length and Post-Graduate Salary

A career advisor is studying whether the length of graduate programs (in years) is related to the me

Temperature and Ice Cream Truck Sales

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

Vehicle Weight and Fuel Efficiency

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