AP Statistics FRQ Room

Analyzing a Stem-and-Leaf Plot of Weights

A stem-and-leaf plot displays the weights (in kg) of 40 participants in a fitness program as follows

App Usage: Comparing Two Advertising Campaigns

A mobile app company ran two advertising campaigns. In Campaign 1, 400 out of 800 users clicked the

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 $$

Blood Pressure Analysis in Clinical Trial

A clinical trial studying a new treatment records the blood pressure of 19 patients. The sample has

Bootstrap Simulation of the Sampling Distribution of the Median Salary

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

College Graduation Rate Analysis

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

Comparing Sleep Hours: High School vs College

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

Data Entry Error and its Impact on Summary Statistics

A delivery company recorded the number of deliveries in a day. The correct data set is: {50, 55, 60,

Distribution Shape and Confidence Interval Interpretation

A survey of 100 car owners reveals that the cars’ mileages have a mean of $$60000$$ miles and a medi

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 Drug

A clinical trial is conducted to evaluate the effectiveness of a new drug in improving patient outco

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

Home Run Distances Analysis

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

Impact of an Outlier on Summary Statistics

Consider the data set $$\{4, 5, 6, 7, 50\}$$. Answer the following:

Impact of an Outlier on Summary Statistics

Consider the data set: {22, 25, 27, 30, 32, 150}, where the value 150 is a potential outlier. Answer

Interpreting Boxplots for Salary Data

A survey of 50 teachers provided salary data summarized in the following boxplot: - Minimum: $30,0

Measures of Variability in Teacher Ages

The ages of 12 mathematics teachers at a high school are: {24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 5

Nature Exposure and Mood Improvement

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

Online Retail Customer Spending Analysis

An online retail store collects data on customer spending. In a sample of 60 customers, the mean spe

Online Shopping Preference by Age Group

An online survey collected responses about shopping behavior by categorizing respondents into age gr

Opinions on School Start Times

Two high schools surveyed their students to determine whether they favor a later school start time.

Restaurant Wait Time Analysis

A consumer group claims that a certain fast-food restaurant’s average wait time is 4 minutes. They c

Sampling Distribution of the Median for Home Run Distances

A baseball analyst collects data on home run distances (in feet) from 13 ballparks: {387, 400, 400,

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

Social Media Usage and Employee Productivity

A business is interested in evaluating whether limiting social media usage during work hours increas

Stock Price Trends Through Parallel Boxplots

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

Temperature and Reaction Rate Regression

A chemical kinetics experiment measured the reaction rate (in mol/sec) at different temperatures (in

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 vs. Ice Cream Sales

An ice cream shop collected data over a summer month to assess the relationship between daily temper

Assessing a New Drug's Efficacy

A clinical trial was conducted to determine the effect of a new drug's dosage (x, in mg) on patient

City Bicycle Usage Study

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

Comparing Marginal and Conditional Distributions in a Two-Way Table

A car dealership survey recorded data on car color and type. The dealership is interested in the dis

Comparing Two Regression Models for Chlorophyll Content Prediction

A biologist is studying the relationship between light intensity (x) and chlorophyll content in leav

Complex Survey Analysis: Income and Expenditure Patterns

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

Consumer Beverage Preference Analysis

A fast‐food restaurant collected data on customer ordering preferences regarding dining style (Dine‐

Cuteness Factor Study Revisited

A Japanese study collected data on 250 volunteers who were shown pictures of cute baby animals, adul

Designing an Observational Study: Screen Time and Sleep Quality

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

Effects of Dropping a High-Leverage Observation

A dataset of 12 observations is used to fit a linear regression model predicting a response variable

Fitness Program Enrollment

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

Fitness Tracker: Step Count vs Active Minutes

A fitness tracking app collected data from 50 users on daily step count (in thousands) and active mi

Green Energy Adoption and Energy Savings

Data from 35 households were analyzed to study the relationship between the percentage of energy fro

Housing Prices and Home Size

A study of 40 houses produced the regression equation $$\hat{y}=50+0.15x$$ predicting house price (i

Interpreting a Simple Linear Regression Model in Advertising

A company studies the relationship between advertising spending (in $1000s) and sales revenue (in $1

Interpreting the Sign and Magnitude of the Correlation Coefficient

A study examining the relationship between daily temperature (X) and ice cream sales (Y) finds a cor

Local Policy Impact: Public Transportation and Commute Times

A city council is evaluating the effectiveness of recent public transit improvements. They collected

Monte Carlo Simulation: Effect of Nonlinearity on Pearson's Correlation

A statistician uses Monte Carlo simulation to explore how nonlinearity in data affects the sampling

Nonparametric Alternatives to Linear Regression

Sometimes the assumptions of linear regression (such as linearity and homoscedasticity) are violated

Pharmaceutical Dosage Testing

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

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

Retail Store: Age and Spending Patterns

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

Sampling Distribution of Exam Scores

Exam scores at a college are normally distributed with a mean of $$75$$ and a standard deviation of

Sampling Distribution of the Coefficient of Determination (\(r^2\)) via Simulation

Researchers study the relationship between study time and exam scores and want to understand the sam

Scatterplot Analysis: Teen Social Media Usage

A study collected data on the number of close friends (X) a group of teens reported and the number o

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

Sports Performance: Height vs. Weight Analysis

A sports analyst collected data on the heights (in inches) and weights (in pounds) of athletes. The

Study Habits and Exam Pass Rates

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

Study Hours and Exam Scores

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

Website A/B Testing for Click-Through Rates

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

Analyzing a Charity Fundraising Event

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

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

Bias in Random Digit Sampling

A researcher uses random digit dialing to contact households for a survey. However, certain demograp

Cluster Sampling in Educational Testing

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

Comparative Simulation of the Mean and Median Sampling Distributions

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

Comparing Sampling Variability Across Methods

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

Designing a Prospective Study on Exercise and Stress Reduction

A local fitness center aims to study the impact of a new exercise regimen on reducing stress levels

Designing a Randomized Controlled Trial for a New Drug

A pharmaceutical company is preparing to test the efficacy of a new drug intended to lower blood pre

Double-Blind Experiment Design for Nausea Reduction

A research team is testing a new wristband designed to reduce postoperative nausea. To eliminate pla

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

Effectiveness of Stress Reduction Methods: Yoga vs. Meditation

A wellness center studied the effectiveness of yoga and meditation on reducing stress. In the yoga g

Environmental Pollution and Respiratory Health

Public health officials are studying the relationship between exposure to particulate matter (PM2.5,

Evaluating the Effectiveness of a New Drug

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

Evaluation of Experimental Design and Inference in Consumer Behavior Studies

A market research study investigates the effect of different advertising strategies on consumer purc

Film Ratings Analysis

A movie review aggregator collects ratings on a scale from 1 to 10 from a simple random sample of 80

Identifying and Mitigating Response Bias in a Health Survey

An online health survey asks participants about sensitive lifestyle behaviors such as alcohol consum

Impact of a Training Program on Employee Productivity

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

Impact of Advertising on Sales Increase

A company wants to evaluate if exposure to an advertising campaign affects the likelihood of an incr

Investigating Effects of Population Variability on Sampling Distributions

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

Investigating Response Time in Emergency Calls

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

Observational Study on Dietary Habits and Exam Performance

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

Online Tutoring and Student Performance

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

Public Health Intervention on Smoking Cessation

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

Retail Customer Purchase Binomial Model

A retailer estimates that the probability of a customer making a purchase during a visit is 10%. On

Retrospective Study on Environmental Exposure and Health Outcomes

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

Sampling Distribution in Voter Polling

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

Simulating the Sampling Distribution of Exam Scores

A teacher is interested in understanding the variability of exam scores in her class. The population

Urban Green Spaces and Air Quality

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

Weather Patterns and Traffic Accidents

City officials are investigating the relationship between adverse weather conditions and the frequen

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:

City Traffic Speed Analysis

The city transportation department collected data on the speeds of vehicles on a major highway. A ra

Cumulative Distribution Analysis of AP Exam Scores

The following table shows the distribution of scores on an AP Statistics exam:

Cumulative Distribution Function Analysis for Daily Customers

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

Employee Training and Department Performance

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

Error Rates in Manufacturing by Shift

A manufacturing plant recorded error types during different shifts. The data is summarized below: |

Geometric Distribution in Reliability Testing

A machine in a factory has a 5% chance of failing on any given day. Let $$X$$ denote the day on whic

High School SAT Scores Analysis

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

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

Investigative Study on Public Health Intervention

A local government is assessing the effectiveness of a new public health campaign aimed at reducing

Medical Treatment Recovery Rates Comparison

A clinical trial compared two treatments for a particular medical condition. Treatment A was adminis

Mobile App Daily Engagement

A mobile app developer claims that at least 40% of users engage daily with the app. In a random samp

Simulated Sampling Distribution of Survey Proportions

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

Simulating the Expected Value in a Lottery Game

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

Student Majors and Graduation Outcome

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

Survey Response Binomial Analysis

In a survey of $$50$$ respondents, each respondent has a $$0.65$$ probability of giving a positive r

Analyzing Differences in Means Between Two Machines

Two machines produce metal rods. Machine A produces rods with a mean length of $$20$$ cm and a stand

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

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

Comparing Teaching Methods

A study compares the effectiveness of two teaching methods. For classes using Method A, test scores

Comparing Variability: Averages versus Individual Values

In environmental testing, individual measurements of a pollutant level exhibit high variability. A s

Critical Values for Beverage Fill Weights

A beverage company claims that its bottles contain 1 liter of liquid on average with a standard devi

Difference in Sample Proportions: Restaurant Experiment

In an experiment to study the effects of environment on eating habits, scientists revamped one of tw

Differences in Daily Step Count due to Wellness Program

A company introduced a wellness program and wants to assess its impact on daily step counts among it

Differences in Sample Means for Weight Loss Program

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

Effect of Sample Size on Variability

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

Effect of Sample Size on Variability of Estimator

A researcher collects repeated samples from a population with a known mean of $$\mu = 100$$ and stan

Employment Benefits Perception

A company surveyed its employees regarding their perception of employment benefits. The responses ar

Evaluating Customer Satisfaction Proportions

A restaurant chain wants to compare customer satisfaction between two of its locations. At Restauran

Evaluating Estimators for Baseball Weight

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

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

Genetic Mutations in New Fathers

A study estimates that 40-year-old men contribute an average of $$65$$ genetic mutations (with a sta

Graduation Rates by Gender

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

Music Streaming Service Satisfaction

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

New Drug Effect on Blood Pressure Reduction

A clinical trial is evaluating a new drug that is believed to reduce blood pressure. Historically, t

Simulation Study on Sample Variances

A simulation study is conducted to explore the sampling distribution of the sample variance $$s^2$$

Social Media Engagement Proportions

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

Unbiased Estimators: Evaluating Sample Slope

In a study of the relationship between hours studied and exam scores, a simple linear regression is

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

Voting Behavior by Gender

A political study analyzed voting behavior based on gender. The table below displays the counts of m

Widget Lifespan Quality Control

A factory produces widgets with an average lifespan of $$500$$ hours and a standard deviation of $$2

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

Assessing New Advertising Campaign Effectiveness

A company runs a new advertising campaign. Out of 400 customers, 160 made a purchase within 24 hours

Assessing Website Conversion Rate

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

Blood Donation Campaign Study

A local health department funds two different public campaigns to increase blood donation rates. One

Comparing Two Teaching Methods: Confidence Interval for Difference in Proportions

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

Confidence Interval for Difference in Proportions: Homeowners vs. Renters on Energy Efficiency

A survey was conducted to compare the preference for energy efficiency improvements between homeowne

Customer Satisfaction: In-Store vs. Online Shoppers

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

Determining Required Sample Size for Test Power

A public health researcher is testing the claim that the proportion of adults who smoke is less than

Effect of Sample Size on Margin of Error

A researcher is investigating the effect of sample size on the margin of error when estimating a pro

Effectiveness of a Social Media Campaign

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

Employee Promotion Rates

A firm is comparing promotion rates between two departments. In Department A, 150 employees were sam

Health Intervention Program Effectiveness

A public health agency is evaluating a new intervention designed to increase the proportion of indiv

Health Study: Smoking Prevalence Comparison

A health study compared the smoking prevalence between two cities. In City A, a sample of 500 respon

Hospital Safety Initiative Comparison

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

Hypothesis Testing for Brand Satisfaction

A company claims that 85% of its consumers are satisfied with its product. A random survey of 200 cu

Interpreting a Confidence Interval

A study on dietary habits produces a 95% confidence interval for the proportion of adults consuming

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.

Investigative Analysis of Consumer Behavior

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

Margin of Error Analysis in a Health Survey on Vaccination Acceptance

A health department surveys 800 random individuals about their willingness to receive a new vaccine;

Marketing Campaign Response Rate Test

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

Measuring Customer Preferences

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

Online Advertising Impact Study

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

Online Shopping Proportion Analysis

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

Political Polling: Estimating Voter Support

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

Public Health: Smoking Rates by Region

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

Retail Coupon Usage Among Customers

Two retail outlets want to know if they differ in the rate of coupon usage among their customers. Ou

Service Reliability Study Analysis

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

Social Media Influence Study

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

Sports Participation by Gender and Sport Type

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

Survey on Remote Work Satisfaction

A technology firm conducted a survey on remote work satisfaction among its employees. Out of 400 res

Test of a Hypothesis on Voter Turnout

A political analyst claims that at least 60% of registered voters participate in elections. A sample

University Policy Support Analysis

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

Urban vs. Rural: Survey on Public Transportation Usage

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

Accident Frequency Comparison

An assembly plant records the number of accidents per month in two independent departments over 30 m

Average Household Electricity Usage

An energy study reports that for a random sample of 40 households, the average monthly electricity u

Battery Life Analysis for a Smartphone Model

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

BMI and Systolic Blood Pressure Analysis

The scatterplot below shows data on body mass index (BMI, x-axis) and systolic blood pressure in mmH

Caffeine Consumption and Reaction Times

A study aims to determine whether the consumption of caffeine affects reaction times. Two independen

Change in Manufacturing Process: Product Lifespan

A manufacturing company claims that a new manufacturing process increases the lifespan of its produc

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 Average Wait Times at Two Coffee Chains

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

Comparing Free-Throw Percentages of Two Basketball Teams

A sports analyst collects data on free-throw percentages of players from two basketball teams. For T

Comparing Two Diets

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

Comparison of Pollutant Concentration in Two Rivers

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

Effect of a New Diet on Weight Loss

A nutritionist is evaluating a new diet plan by measuring the weight loss of 24 participants over a

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

Effectiveness of a New Drug on Pain Relief

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

Fuel Consumption and Distance Traveled Analysis

The scatterplot below displays data on the gallons of fuel used (x-axis) and the corresponding dista

Fuel Efficiency Analysis

A study is conducted to assess the fuel efficiency (in miles per gallon) of a new model of cars. A r

Hospital Stay Duration Comparison

A hospital administration is examining the average length of patient stays in two independent units:

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

Impact of Advertising on Product Awareness

A marketing team wants to analyze the effect of advertising on product awareness. Consumers are cate

Manufacturing Measurement Variability

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

Medical Test Accuracy and Diagnosis

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

Online Shopping and Customer Satisfaction

A retail company conducted a survey to assess customer satisfaction with its online shopping experie

Pre- and Post-Treatment Blood Pressure Analysis

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

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

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 Average Household Income

An economist is studying household incomes, which are known to be right-skewed. The economist uses s

Test Score Comparison between Two Classes

Two different classes took a standardized test. Class A (n = 30) had a mean score of 78 with a stand

Test Score Improvement Analysis in a Preparation Class

In an SAT preparation class, 25 students took a pre-test and a post-test. The improvements (post-tes

Testing Mean Daily Coffee Consumption Claim

A claim is made that college students drink an average of at least 2.5 cups of coffee per day. A sur

Voting Behavior and Political Affiliation

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

Advertising Channels Effectiveness: Homogeneity Test

A company wants to determine if the effectiveness of three advertising channels (TV, Online, Print)

Association between Exercise Frequency and Diet Type

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

Bike-Sharing User Gender Distribution Goodness-of-Fit Test

A bike-sharing company claims that the gender distribution of its users is 60% male and 40% female.

Customer Satisfaction Survey Across Store Locations

A retail company conducts a survey to assess customer satisfaction across three store locations: Nor

Customer Service Feedback in Retail Stores: Homogeneity Test

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

Distribution of Housing Types in a City

A city planning department is examining the distribution of housing types in the city. They expect t

Drug Efficacy Across Regions: Homogeneity Test

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

Effectiveness of a New Training Program across Branches

A company implements a new training program in three of its branches. After the program, employees a

Evaluating Student Performance: Chi-Square Goodness-of-Fit in Grades Distribution

A large high school believes that the distribution of final letter grades (A, B, C, D, F) on a stand

FRQ 13: Customer Loyalty Across Store Branches

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

Genetic Trait Distribution Goodness-of-Fit

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

Genetics Research: Rat Coat Colors

In a genetics experiment, the expected Mendelian ratio for rat coat colors is 3:1 (dominant: recessi

Goodness-of-Fit for Beverage Preferences

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

Homogeneity in Dietary Habits Across Regions

Nutrition researchers surveyed individuals from three regions regarding their dietary habits: Omnivo

Independence Test: Dietary Supplements and Energy Levels

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

Independence Test: Voting Preference and Gender

A survey of 500 voters collected data on voting preference (Candidate A, Candidate B, Other) and gen

Quality Control in a Factory

A factory has three production lines, each producing 100 items. Quality control involves checking fo

Quality Control in Manufacturing

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

Simulated Chi-Square Distribution for Voting Patterns

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

Social Media Platform Usage

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

Socioeconomic Status and Book Reading Frequency: Independence Test

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

Sports Preferences by Gender: Chi-Square Test for Independence

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

Student Enrollment by Gender and Major: Chi-Square Test for Independence

A university is investigating if student major (STEM, Arts, Business) is independent of gender (Male

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

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

Advertising Budget and Revenue

A study on 25 companies examines the relationship between advertising budget (x, in thousands of dol

Advertising Spending and Sales Revenue

A company collected data on its monthly advertising spending (in thousands of dollars) and correspon

Air Quality and Traffic Flow

A study investigates whether daily traffic flow (vehicles per hour) is associated with urban air pol

City Population and Public Transportation Usage

A city planner is investigating whether there is a linear relationship between city population (in t

Coffee Consumption and Alertness

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

Coffee Consumption and Alertness

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

Daily Steps vs Calorie Burn

A fitness app developer examined the relationship between the number of daily steps and calorie burn

Effect of Study Intervention on Academic Performance

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

Employee Performance from Experience

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

Engine Size and Fuel Efficiency

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

Environmental Study: Pollutant Concentration and Respiratory Issue Rates

Researchers are studying the impact of pollutant concentration (in parts per million, ppm) on the ra

Exercise Time and Calorie Burn

A fitness app tracks the number of minutes spent exercising (x) and the number of calories burned (y

Global Temperature Change

A climatologist studies the relationship between time (measured as years since 1900) and the average

House Size vs House Price

A real estate analyst is studying the relationship between house size (in square feet) and house pri

Influence of Advertising Budget on Sales

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

Marketing Strategy and Customer Visits

A retail chain implemented a new marketing strategy and analyzed its effect on the number of custome

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 and Recovery Time

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

Regression Analysis in Real Estate Pricing

This question examines inference for the slope in a linear regression analysis between living area (

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 Usage vs GPA

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

Temperature Effects on Motor Speed

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

Urban vs Rural Pollution Levels

An environmental study examined the relationship between daily traffic volume (in thousands of vehic

Weather Forecasting: Humidity vs. Chance of Precipitation

Meteorologists studied the relationship between relative humidity (x, in percentage points) and chan

Weather Prediction Model: Slope Simulation

A climatologist is using simulation to explore the relationship between time of day (in hours) and t

Weight Loss and Diet Adherence

A nutritionist is studying the relationship between the number of diet counseling sessions attended