AP Statistics FRQ Room

Advertising Campaigns and New Customer Sign-ups

A company ran two advertising campaigns to increase new customer sign-ups. In Campaign 1, there were

Analysis of Categorical Data from Elections

A recent survey sampled 1000 voters to determine their preferred candidate in a local election. The

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: |

Boxplot Construction from Exam Scores

Consider the following set of exam scores: $$\{15, 18, 22, 24, 24, 25, 27, 29, 30, 32, 35\}$$ Answ

Cafeteria Food Satisfaction Proportion

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

Car Price and Mileage Regression Analysis

A used-car dealership analyzes data from 80 vehicles to predict the selling price (in thousands of d

Comparing Exam Score Distributions

Two classes took the same exam and their performances are summarized with back-to-back stemplots. Al

Customer Ratings for Two Products

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

Customer Satisfaction in Retail Chain

A retail chain surveyed 250 customers regarding their satisfaction level (Satisfied, Neutral, Dissat

Customer Service Call Duration

Customer service call durations are approximately normally distributed with a mean of $$8$$ minutes

Customer Service Satisfaction by Service Type

A company surveyed 550 customers on their satisfaction level (Satisfied, Not Satisfied) with three t

Distribution of Heights in a Grade

A study on the heights (in centimeters) of students in a particular grade produced the following fre

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

Dotplot Representation of Home Run Distances

A dotplot displays the following frequencies for home run distances (in feet): • 387 appears once •

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

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 Study Methods on Exam Performance

A school district plans a study to determine whether group study or individual study leads to higher

Interface Redesign and User Engagement

A tech company is testing whether a software interface redesign leads to higher user engagement. Use

Irrigation Techniques and Crop Yield

An agricultural study is set up to compare three irrigation techniques (drip, sprinkler, and flood)

New York City Taxi Mileage Distribution

Taxicabs in New York City are driven an average of 75,000 miles per year with a standard deviation o

Normal Distribution: Taxi Mileage

Taxicabs in a large city are driven an average of $$75000$$ miles per year with a standard deviation

Online Course Satisfaction Hypothesis Test

A university is evaluating the satisfaction level with its online course. In a survey of 200 randoml

Product Length Variability in Manufacturing

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

Product Return Rates Across Regions

A company tracks product returns across four regions (North, South, East, West) with outcomes 'Retur

Remote Learning Preference in High Schools

Two high schools surveyed their students regarding their preference for remote learning. In School A

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

Teacher Age Distribution Analysis

The ages (in years) of 12 mathematics teachers are given as follows: {24, 25, 25, 29, 34, 37, 41, 42

Weekly Exercise Sessions

Assume that on any given day, a person exercises for at least 30 minutes with a probability of $$0.4

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

Advertising Spend and Sales Revenue

A company collected monthly data over one year on its advertising expenditure (in thousands of dolla

Analyzing a Survey on Social Media Use and Sleep

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

Analyzing Curvilinear Relationship and Data Transformation

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

Calculation of Correlation and Linear Regression from Summary Statistics

A study examines the relationship between daily device usage (in hours, X) and a productivity score

Car Crash Safety Feature Evaluation

An automotive safety engineer evaluates two car models based on their performance in crash tests. Th

City Bicycle Usage Study

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

Coffee Shop Sales Analysis

A local coffee shop has recorded data on daily advertising expenditure (in dollars) and the correspo

Complex Survey Analysis: Income and Expenditure Patterns

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

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 between Exercise and Weight Loss

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

Customer Satisfaction Comparison at Two Store Branches

A retail company collected customer satisfaction data from two store branches, Branch A and Branch B

Dosage and Blood Pressure Reduction

In a clinical trial with 25 patients, the relationship between drug dosage (in mg) and reduction in

Effectiveness of a Medical Treatment

A clinical trial is designed to evaluate the effectiveness of a new cholesterol-lowering drug. Patie

Free Throw Performance in Basketball

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

Housing Renovation Impact on Property Values

A real estate researcher is investigating whether the cost of home renovations (x, in thousands of d

Quality Control in Manufacturing

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

Relationship between Study Hours and Test Scores

A study investigates the relationship between the number of hours students study per week and their

Residual Analysis in House Price Prediction

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

Restaurant Service and Tipping

A restaurant manager collected data on the wait time (in minutes) experienced by customers and the c

Restaurant Tip Analysis

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

Retail Promotions: Sales vs Advertising Budget

A retail chain recorded weekly data (n = 20) on advertising budget (x, in thousand dollars) and week

Simulation Study for Confidence Intervals in Linear Regression Predictions

A marketing analyst uses simulation to assess the performance of confidence intervals in predicting

Analysis of Smoking Habits Among Adults

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

Analyzing Sampling Variability with Box Plots

A study is conducted to estimate the average test score for teachers in a school district. Four diff

Analyzing Survey Bias in Voluntary Response Surveys

A local newspaper conducts a voluntary response survey asking residents about their satisfaction wit

Clinical Trial on Weight Loss Programs

A randomized controlled trial compares two weight loss programs. Program A (n = 40) results in an av

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 Prospective and Retrospective Data Collection in Education Studies

A school district wants to study the impact of extracurricular activities on academic performance. T

Comparing Sampling Variability Across Methods

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

Comprehensive Analysis of Consumer Behavior in Response to Online Advertisements

A consumer goods company wants to study how online advertisements influence purchasing behavior. The

Designing a Double-Blind Experiment for a New Drug

A pharmaceutical company intends to test a new drug aimed at reducing blood pressure. To eliminate b

Designing a Prospective Study for Teaching Methods

A school district wants to study the effect of a new teaching method on student performance on stand

Designing a Representative Student Survey

A university desires to survey its 10,000 students about campus dining experiences. To ensure repres

Hypergeometric Distribution in Quality Inspection

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

Impact of a Training Program on Employee Productivity

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

Impact of Diet on Weight Loss Success

A nutritionist compared the success rates of two different diet plans. Under Diet A, 45 out of 75 pa

Investigating Response Time in Emergency Calls

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

Online Ad Click-Through Rates and Sampling Distributions

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

Physical Activity and Cognitive Function in Older Adults

Researchers are investigating whether increased physical activity is associated with better cognitiv

Public Health Intervention on Smoking Cessation

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

Remote Learning and Student Engagement

A school district wants to evaluate the effectiveness of remote learning on student engagement. Data

Replication in an Agricultural Experiment

An agricultural scientist is testing the effectiveness of two fertilizers on crop yield. The experim

Retail Store Checkout Efficiency Study

A study compared the average waiting time at checkout between two methods in a retail store. For the

Sampling Distribution in Voter Polling

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

Social Media Usage among Teenagers

A survey of teenagers collected data on social media platform preferences (Instagram, Snapchat, TikT

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

Volunteer Firefighter Response Times

A prospective study of volunteer firefighter response times records data from 45 incidents. The samp

Binomial Distribution in Lightbulb Defectiveness

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

Casino Free Chips Expected Sum

A casino offers free chips to couples. One person draws a card from Bag X containing the numbers $$\

Charity Lottery Expected Value Analysis

A charity sells 10,000 lottery tickets at $$\$1$$ each. One ticket wins a prize of $$\$7500$$, while

City Traffic Speed Analysis

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

Comparing Click-Through Rates of Two Advertising Campaigns

An online ad campaign was run using two different strategies. Campaign A achieved 210 clicks from 30

Comparing Simulation Results for Rainy Days

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

Drug Effectiveness Study

Researchers conducted a clinical trial comparing a new drug to a placebo. The recovery outcomes are

Effect of Fertilizer Type on Plant Growth

An agricultural researcher is studying the effects of three different fertilizer types on plant grow

Effectiveness of Public Health Announcements on Mask-Wearing Behavior

During a flu outbreak, a health department launches a public health campaign to encourage mask-weari

Event Planning and Rainy Days: Binomial Analysis

An event planner considers a month of 30 days where the probability of a rainy day is $$0.3$$, indep

Geometric Distribution: Encountering an Honest Man

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

Highway Construction Productivity Analysis

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

Hospital Stay Durations Analysis

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

Impact of Meditation on Stress Reduction

A mental health clinic is studying whether an 8‐week meditation program reduces stress levels in its

Medication Dosage and Recovery Time Regression Analysis

A clinical study investigates the effect of medication dosage (in mg) on patient recovery time (in d

Multistage Probability: Computer Viruses

On a university campus, computers run on different operating systems with the following distribution

Predicting Blood Glucose from Hemoglobin A1c Levels

A study examines the relationship between Hemoglobin A1c levels (in %) and blood glucose (in mg/dL)

Public Opinion Survey on Local Issues

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

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

Simulation in Hypothesis Testing: Generating a Reference Distribution

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

Simulation of the Law of Large Numbers in Practice

A simulation is conducted using a biased die that shows a '6' with a probability of $$0.7$$. The die

Startup Daily Profit Analysis

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

Tip Amounts from Different Meal Services

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

University Dining Hall Food Quality Survey

A survey of university dining hall patrons was conducted to assess food quality. Out of 200 responde

Virus Spread Modeling among Animal Species

A study examines the spread of a virus among three animal species with the following data: | Specie

Website Navigation and Conversion Rates

A website conducted an A/B test with two versions (A and B) and recorded visitor conversion outcomes

Website Server Demand Modeling

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

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

Assessing Estimators for Baseball Weight

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

Caffeine Content Analysis in Energy Drink Boxes

An energy drink contains caffeine distributed with a mean of 200 mg and a standard deviation of 10 m

Caffeine Content in Energy Drink Boxes

A store sells boxes containing six bottles of an energy drink. The caffeine content per bottle is no

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

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

Dream Recall Simulation Study

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

Effect of New Teaching Method on Student Scores

A school district is testing a new teaching method. Two groups of students are studied: a control gr

Effect of Sample Size on Sampling Variability

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

Employment Benefits Perception

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

Estimating Average Commute Time

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

Estimator Evaluation in Baseball Manufacturing

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

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

Hypothesis Testing for a New Drug's Effect on Blood Pressure

A clinical trial is conducted to test the claim that a new drug reduces blood pressure by 10 mmHg. I

Impact of Sample Size on Variability

A researcher is analyzing daily website visits. In an initial study with 30 days, the sample standar

Normal Approximation Conditions for Solar Panel Households

A survey finds that 9% of households have solar panels. A random sample of 150 households is selecte

One-Sample vs. Two-Sample Sampling Distributions

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

Polling Data Analysis

In a large election, the true support for a candidate is believed to be $$52\%$$. A random sample of

Quality Control of Widget Weights

A factory produces widgets with weights that are normally distributed with $$\mu = 100$$ grams and $

Regional Customer Satisfaction Analysis

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

Sample Size Calculation for Voter Support Estimation

A political survey aims to estimate the proportion of voters supporting a specific candidate with a

Sample Size Effects: Simulation Analysis

A simulation study is performed to examine the effect of sample size on the variability of the sampl

Simulation of Sampling Distributions for Medians

A recent survey of high school students examined the number of hours studied per week. Although the

Student Extra-Curricular Participation

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

Unbiased Estimators: Evaluating Sample Slope

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

Advertising Impact on Brand Recognition

A company runs a new advertisement in two regions. In Region 1, 210 out of 350 respondents recognize

Assessing Customer Satisfaction in a Retail Store

A retail store surveys 200 customers and finds that 150 are satisfied with their shopping experience

Assessing Website Conversion Rate

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

Business Model Customer Return Rate Comparison

A company compares two business models by examining customer return rates. For Model A, 312 out of 5

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

Comparing Voter Turnout between Two Regions

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

Consumer Preference: Hypothesis Testing for a Single Proportion

A company claims that at least 40% of consumers prefer its new product. In a sample of 250 consumers

Customer Satisfaction: In-Store vs. Online Shoppers

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

Drug Effectiveness: Hypothesis Testing for Proportion

A clinical trial involving 200 patients found that 154 recovered after treatment with a new drug. Th

Effectiveness of a Drug

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

Election Poll Margin of Error Analysis

An election poll reports a candidate's support proportion as 0.48 with a margin of error of 0.04 at

Environmental Study: Testing Proportion Exceeding Safety Threshold

A study of water quality in a river found that 18 out of 90 samples exceeded the safety threshold fo

Estimating Social Media Usage Proportions

A research study surveyed 750 social media users to estimate the proportion who use a specific app d

Ethnicity and University Major

A university survey collected data on student major (STEM vs. Humanities) and ethnicity (Underrepres

Health Survey Confidence Interval Analysis

A local health department conducted a survey regarding residents' compliance with a new health regul

Healthcare Plan Satisfaction

A survey was conducted among employees to assess satisfaction with their healthcare plans. Participa

Impact of Training Program on Certification Rates

A company implemented a training program to improve certification rates among its employees. In a ra

Investigative Analysis of Consumer Behavior

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

Medical Trial: Comparing Treatment and Control

A clinical trial compares the effectiveness of a new treatment with a placebo. In the treatment grou

Online Shopping Fraud Claims

An online survey compares the percentage of consumers who reported experiencing fraudulent transacti

Online Shopping Proportion Analysis

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

Public Library Usage Survey

A city council conducted a survey to determine the proportion of residents using the public library.

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

Public Transit Usage

A city planning study compares the proportion of residents using public transit in two cities. City

Research on Smoking Cessation Program

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

Retail Store Customer Satisfaction Confidence Interval

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

Smoking Status and Respiratory Illness

Hospital records show data on patients' smoking status and whether they have a respiratory illness.

Vaccine Hesitancy Survey Design

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

Voter Approval Poll Design

A polling organization samples voters to estimate the proportion of the electorate that approves of

Assessing a New Teaching Method

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

Battery Life Study

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

Career Development Program

A corporation has implemented a career development program and wishes to assess its impact on employ

Coffee Consumption and Alertness Scores

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

Comparative Analysis of Lecture Techniques Using Paired Data

A study compares two lecture methods implemented on the same group of 30 students. The students take

Comparing Manufacturing Processes

A company uses two different processes to manufacture a particular part. Process X is evaluated on a

Comparing Two Diets

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

Customer Satisfaction Survey

A popular online retailer claims an average customer satisfaction rating of 8.5 (on a 10-point scale

Diet Program Effectiveness

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

Education and Annual Income Analysis

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

Effectiveness of Drug Treatments

A clinical trial compares two drug treatments (Drug X and Drug Y) for a certain condition. Patients

Energy Consumption Analysis

An energy company is testing the claim that the average daily electricity consumption of households

Evaluation of New Teaching Method Using Paired Data

An educational researcher investigates the impact of a new teaching method on student performance. A

Exercise and Resting Heart Rate Analysis

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

Fuel Consumption and Distance Traveled Analysis

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

Hospital Stay Duration Comparison

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

Impact of Advertising on Product Awareness

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

Impact of Variability on Confidence Intervals: A Simulation Study

A simulation study is conducted to explore how differences in sample variability affect the width of

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

Math Test Scores and Teaching Methods

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

Pre- and Post-Treatment Blood Pressure

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

Pre-Test and Post-Test Scores Analysis

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

Production Time and Number of Defects Analysis

The scatterplot below displays data on production time in minutes (x-axis) and the number of defects

Quality Control in Production

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

Reaction Time Testing Under Caffeine Effects

A study examines the effect of caffeine on human reaction times. Two independent random samples of 2

Recovery Rates in Two Hospitals

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

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 Mean Crop Yield

An agricultural researcher is interested in the average crop yield (bushels per acre) of a particula

Sodium Intake and Systolic Blood Pressure Analysis

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

Soil pH Variation

An agricultural experiment is conducted to assess whether a new fertilizer treatment helps bring soi

Student Participation in Extracurricular Activities

Researchers are studying the relationship between club membership and academic achievement in a samp

Study of Daily Traffic Flow

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

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

Testing Mean Daily Water Consumption

A municipal claim states that the mean daily water consumption in a city is 150 liters. A survey of

Weight Loss Confidence Interval

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

Adoption Rates of Electric Vehicles by Region

A study compares the adoption rates of electric vehicles in three different regions: Urban, Suburban

Analysis of Dietary Habits

A nutrition study investigates whether dietary preferences are homogeneous across four regions. The

Association between Exercise Frequency and Diet Type

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

Blood Type Distribution: Goodness-of-Fit Test

A study of 400 individuals reports the following observed counts for blood types: O = 180, A = 120,

Coffee Preference in College

Three colleges conducted surveys of 150 students each to determine their preferred type of coffee: E

Customer Response to Advertising: Chi-Square Test for Independence

A company’s advertising campaign is evaluated by surveying customers on their response (Positive, Ne

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,

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

Drug Side Effects Analysis: Chi-Square Test for Independence

In a controlled clinical trial, researchers are investigating whether the frequency of certain side

Effect of Marketing Campaign on Brand Awareness

A company wishes to determine if exposure to its marketing campaign is associated with brand awarene

Employee Training Program: Comparing Certifications Across Departments

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

Favorite Ice Cream Flavor Goodness-of-Fit Test

A market survey hypothesizes that the favorite ice cream flavors are distributed as: Chocolate 40%,

FRQ 1: Distribution of Customer Preference for a New Snack

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

FRQ 6: Association Between Diet and Heart Disease Risk

A study investigates whether there is an association between diet type and heart disease risk. The s

FRQ 7: Comparing Satisfaction Levels Across Service Centers

A company wants to determine if customer satisfaction is consistent across three service center bran

FRQ 13: Customer Loyalty Across Store Branches

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

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

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 Trait Distribution Goodness-of-Fit

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

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

Online Shopping Day Preferences: Chi-Square Goodness-of-Fit

A retailer surveys 150 online shoppers to determine which day of the week (Monday through Friday) th

Product Preference Independence Test by Gender

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

Quality Control: Defective Items in Production Lines

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

Restaurant Popularity Goodness-of-Fit

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

Smoking and Lung Disease: Independence Test

A survey of 300 individuals reports the following counts: Smoker with lung disease = 40, Smoker with

Species Distribution in a Wildlife Reserve

In a wildlife reserve, the theoretical model predicts that the species distribution should be: Mamma

Sports Participation and Gender – Chi-Square Test for Independence

A school conducted a survey to examine the relationship between gender (Male, Female) and participat

Test for Independence: Political Opinions on Climate Change

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

Voting Behavior and Demographics

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

Workplace Safety Incidents: Chi-Square Test for Independence

In a manufacturing plant, data on safety incidents are collected and classified by type (Minor, Seri

Annual Rainfall and Crop Yield

An agricultural researcher is examining the relationship between annual rainfall (x, in inches) and

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

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

Coffee Consumption and Anxiety Levels

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

Effect of Study Intervention on Academic Performance

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

Electricity Bill vs Temperature

A utility company studied the relationship between the average monthly temperature (in $$^\circ F$$)

Exercise Duration and Weight Loss

A fitness study explores the relationship between exercise duration (in minutes) and weight loss (in

Exercise Duration vs Heart Rate

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

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

Housing Price Estimation

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

Ice Cream Sales and Temperature

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

Internet Speed vs. Streaming Delay

A study of 30 households examines the relationship between internet speed (in Mbps) and video stream

Manufacturing Quality Control: Regression Parameter Optimization Simulation

A quality control engineer is analyzing the relationship between machine operating speed (in m/s) an

Mobile App Usage Study

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

Online Advertisement View Time and Purchase Likelihood

A study examines the relationship between the time spent viewing an online advertisement ($$x$$, in

Predicting Student Performance with Attendance Rates

A teacher collects data on student attendance rates (x, in percentage) and corresponding performance

Rainfall vs Crop Yield

An agricultural economist is investigating the relationship between annual rainfall (in inches) and

Relationship Between Stress Level and Reaction Time

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

Social Media Use and Academic Performance

A study examines whether daily social media usage (x, in hours) is related to students' GPAs (y, on

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

Technology Training and Productivity

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