AP Statistics FRQ Room

Bootstrap Simulation of the Sampling Distribution of the Median Salary

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

Car Fuel Efficiency Test

A study measures the fuel efficiency of a sample of 50 cars. The sample has a mean miles per gallon

College Admissions Test Scores

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

College vs. High School Sleep Study

Two surveys measured the number of hours of sleep per night. The high school survey recorded the fol

Comparing Cumulative Frequency Graphs for Age Distributions

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

Comparing Measures of Variability: IQR vs Standard Deviation

Consider the data set: {12, 15, 18, 21, 24, 27, 30}. Answer the following:

Comparing Pass Rates for Two Classes

In a high school, two math classes took the same standardized test. In Class 1, 28 out of 35 student

Comparing Sleep Hours: High School vs College

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

Cumulative Frequency Analysis of Age Distribution

A study compares the age distributions of two different years using cumulative frequency plots. In Y

Daily Caloric Intake Data Analysis

A nutrition study collected data on the daily caloric intake of 170 individuals. The results, broken

Dietary Preferences by Gender

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

Effectiveness of a New Drug

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

Evaluating a Histogram for Skewness in Temperature Data

A histogram shows the distribution of daily temperatures (in °F) during a summer month. The histogra

Exploring Daily Sales Data Using a Stem-and-Leaf Plot

A small business has recorded its daily sales (in dollars) over 15 days. The data are summarized in

Medication Efficacy in Reducing Blood Pressure

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

Meditation Training for Stress Reduction

A psychological study is designed to determine if meditation training reduces stress levels among co

Nutrition Study: Effects of Diet on Weight Loss

A nutritionist intends to study whether different diets lead to different average weight losses over

Online Course Satisfaction Hypothesis Test

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

Online Retail Customer Spending Analysis

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

Political Polling: Candidate Preference

In a political poll, two states were surveyed to determine the proportion of voters favoring Candida

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,

Simulated Sampling Distribution of the Standard Deviation

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

Simulation and Transformation Effects on the Sampling Distribution

A researcher studying bacterial growth rates, which follow an exponential distribution, collects dat

Stock Price Outlier Analysis

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

Stock Price Trends Through Parallel Boxplots

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

Survey of Preferred Exercise Modalities

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

Survey Response Methods Comparison

A survey was administered using two methods: telephone and online. In the telephone survey, 115 out

Teacher Ages Analysis

The ages (in years) of 12 mathematics teachers are: $$\{24, 25, 25, 29, 34, 37, 41, 42, 48, 48, 54,

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 Website Traffic

A small business used data from 15 weeks to analyze the effect of advertising spend on website visit

Analyzing Temperature Effects on Electricity Consumption

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

Athletic Performance Correlation Analysis

A study on athletes observed the relationship between hours of training per week (x) and competition

Bootstrapping Confidence Interval for Regression Slope

A small study examines the relationship between annual income (x, in $1000s) and self-reported happi

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

City Bicycle Usage Study

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

Clinic Survey on Treatment Outcomes

A clinical trial was conducted to evaluate treatment effectiveness. Two treatment protocols were adm

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

Effects of Dropping a High-Leverage Observation

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

Evaluating Housing Market Trends Through Transformation

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

Evaluating Public Health Data on Smoking and Lung Cancer

A study was conducted to investigate the association between smoking and lung cancer incidence among

Exploring the Sampling Distribution of the Regression Slope Under Increasing Error Variability

In a study of the relationship between income (x) and expenditure (y), researchers use simulation to

Free Throw Performance in Basketball

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

Internet Usage and Credit Card Fraud

A cybersecurity study examined the relationship between frequency of internet usage and whether indi

Limitations of Simple Linear Regression

Discuss the limitations of using a bivariate (simple linear) regression model when other explanatory

Market Research: Effect of Price on Sales Volume

A company is investigating how the price of their product affects its sales volume. The collected da

Online Course Engagement and Performance

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

Online Course Enrollment Prediction

A university is analyzing the effect of the number of online advertisements (x) on online course enr

Promotion Program Success Comparison

A company implemented two distinct promotional programs to boost sales. In Program 1, 92 out of 150

Simulation of the Mean Residuals in a Regression Model

In a regression analysis, residuals (the differences between observed and predicted values) are expe

Social Media Activity and Face-to-Face Interactions

In a survey of 40 individuals, data were collected on the number of social media posts per week (x)

Social Media Use and Online Privacy

In a study on digital behavior, participants were surveyed about their level of social media usage (

Specialty Coffee Orders at a Coffee Shop

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

Student Study Habits and GPA

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

Temperature and Ice Cream Sales

A study over 30 days recorded the average daily temperature (in °F) and corresponding ice cream sale

Voting Behavior and Media Consumption

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

Willingness to Adopt Electric Vehicles

A market research study investigated whether income level influences the willingness to adopt electr

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 Retrospective and Prospective Studies in Outbreak Analysis

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

Comparing Stratified and Cluster Sampling Methods in a Health Survey

A public health researcher is designing a survey to assess attitudes toward vaccination in a multi-n

Effect of Diet on Cholesterol Levels

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

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

Evaluation of a New Teaching Method

An educational study compared a New teaching method with a Traditional one in terms of student exam

Factorial Experiment on Study Hours and Tutoring

A study is conducted to examine the effects of study hours and tutoring on student test scores. Stud

Influence of Outliers on the Sampling Distribution of the Sample Median

In studies of household incomes, extreme high incomes (outliers) can heavily influence the sample me

Interpreting a Scatterplot from a Survey on Sleep and Test Scores

A study surveys high school students regarding their average nightly sleep (in hours) and their most

Interpreting Observational Study Data on Exercise and Blood Pressure

A study tracks daily exercise minutes and resulting changes in blood pressure for 100 adults over a

Investigating Data Variability in Statewide Math Test Scores

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

Matched Pairs Design in a Dietary Study

A nutritionist wants to compare the effectiveness of two diets on weight loss. To control for initia

Mobile App User Engagement

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

Retail Store Checkout Efficiency Study

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

Retrospective Study on Environmental Exposure and Health Outcomes

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

Simulating Cluster Sampling and its Effects on the Sampling Distribution

A health survey is conducted using cluster sampling by selecting several schools from a district and

Smartphone Usage and Sleep Quality

Examine the relationship between smartphone usage and sleep quality among college students. Research

BMI and Systolic Blood Pressure Regression Analysis

A study investigating the relationship between Body Mass Index (BMI) and systolic blood pressure (in

Car Purchase Decisions by Region

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

Carnival Game of Chance: Payoff Transformations

A carnival game offers different monetary payoffs with the following probabilities: | Payoff ($$\$\

Coin Toss Experiment and Sample Size Effects

Consider an experiment where a fair coin is tossed repeatedly. Answer the following:

Comparing Bank Loan Approval Rates

A bank uses two different underwriting policies. Under Policy A, 300 out of 500 applicants are appro

Comparing Guessing and Knowledge-based Answers

In an exam, if a student guesses an answer, the probability of a correct response is 0.20. If the st

Comparing Patient Wait Times at Two Clinics

Two clinics recorded patient wait times. Clinic 1 (n = 40) had an average wait time of 25 minutes wi

Customer Retention and Marketing Strategies

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

Defective Light Bulb Binomial Probabilities

Suppose the probability that a light bulb is defective is $$0.1$$. Consider independent selections o

Defective Products in Quality Control (Binomial Distribution)

In a quality control process, each product has a defect probability of 0.08 and is inspected indepen

Effects of Outliers on Sampling Distributions

A simulation study involves drawing samples from a dataset that contains outliers. For each sample,

Employee Training and Department Performance

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

Fitness Class Participation by Age Group

A gym surveyed 300 members about their preferred fitness class types. The results by age group are d

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

Geometric Distribution: Encountering an Honest Person

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

Impact of Advertising on Consumer Behavior

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

Insurance Policy Sales Analysis

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

Medical Trial for a New Drug

A pharmaceutical company is conducting a clinical trial to test the efficacy of a new drug in reduci

Mobile App vs. Printed Pamphlet for Increasing Exercise Duration

A public health organization wants to determine whether a mobile app intervention or a printed pamph

Movie Rating Analysis on Streaming Platforms

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

Online Shopping Behavior by Time of Visit

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

Predicting Blood Glucose from Hemoglobin A1c Levels

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

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

Scatterplot Regression Analysis on Study Habits

A researcher collects data on the number of hours students study (x) and their exam scores (y). The

Simulated Distribution of the Difference of Sample Means

In a simulation comparing two independent groups (for example, treatment and control), separate samp

Social Media Post Engagement

A social media analyst is studying the engagement on posts from a popular brand. A random sample of

Television Viewing Habits by Age and Time of Day

A survey of 300 television viewers recorded their preferred viewing times (Morning or Evening) acros

Transformation of Payout Values

A game machine produces a random payout $$X$$ with a mean of $5 and a standard deviation of $3. A re

Transforming Payouts in a Carnival Game

A carnival game pays out according to a random variable $$X$$ with outcomes: $10 (p = 0.4), $20 (p =

Transportation Delay Times

A city's bus service experiences delays (in minutes) according to the following distribution: | Del

Understanding the Central Limit Theorem through Simulation

A simulation is performed where samples are drawn from various non-normal populations (for example,

University Dining Hall Food Quality Survey

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

University Exit Exam Pass Rate

A local university advertises that at least 70% of its students pass the exit exam. In a random samp

Advanced Experimental Design in Teaching Methods

A researcher is investigating the effectiveness of two teaching methods by comparing student test sc

Battery Life Analysis Using Normal Distribution

A battery manufacturer claims that the lifespan of its batteries is normally distributed with mean $

Battery Lifespan Analysis

A company produces batteries whose lifespans (in hours) are normally distributed with $$\mu = 500$$

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

Coffee Consumption and Alertness

A study investigates whether coffee consumption is related to alertness. Two independent samples wer

Comparing Clinical Trial Drug Effects

In a clinical trial, two drugs are used to lower blood pressure. Drug A produces an average reductio

Comparing Customer Satisfaction Among Two Stores

A retail chain conducts a study comparing customer satisfaction levels. In store A, 85% of customers

Comparing Drug Efficacy Using Sample Proportions

A clinical trial is conducted to compare the efficacy of a new drug versus a placebo. It is estimate

Comparing Teaching Methods

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

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 $$1$$

Constructing a 95% Confidence Interval for Battery Lifetime

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

Difference in Sample Proportions: Revamped vs. Unrevamped Restaurant

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

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

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

Estimator Evaluation in Baseball Manufacturing

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

Impact of Sample Size on the Standard Error

Researchers are investigating how sample size affects the variability of the sample mean. From a pop

Lightbulb Life Expectancy Analysis

A certain brand of lightbulbs has a life expectancy that is approximately normally distributed with

Normal Approximation to the Binomial in Sampling Distributions

A factory has a light bulb defect rate of 2%. In a shipment of 500 bulbs, let X represent the number

Normal Distribution Calculation: Component Lifespan

A certain machine component has a lifespan that is approximately normally distributed with mean $$\m

Regression Analysis and Inference in a Health Study

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

Simulated Daily Sales Distribution

A retail store simulated its daily sales over several months. The resulting sampling distribution of

Simulation of Sampling Distributions: Dreams Recorded

A study finds that high school students remember an average of 3.4 dreams per night with a variance

Simulation of the 90th Percentile

A study simulates the sampling distribution of the 90th percentile from a non-normal distribution. A

Social Media Usage by Age Group

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

Social Media Use and Sleep Duration

Researchers investigated the impact of social media use on sleep duration. Two independent groups we

Survey on Learning App Preference

In a high school, it is believed that $$65\%$$ of students prefer using a new learning app. A random

Training Techniques and Marathon Finish Times

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

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

Analysis of Survey Data on Online Learning

A survey of 150 students indicates that 90 prefer online learning. A table summarizing the responses

Analyzing Proportions as a Function of Batch Size

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

Campaign's Voter Turnout Comparison

A political campaign is studying voter turnout in two neighboring cities. In City A, a survey of 400

Comparing Participation Rates in Exercise Programs Across Cities

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

Confidence Interval for a Population Proportion

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

Conservation Program Study

A local government has implemented an environmental conservation program intended to increase the pr

Customer Satisfaction in a Retail Store

A large retail chain conducted a survey to measure customer satisfaction. Out of a simple random sam

Designing a Survey for Voting Behavior

A political researcher plans to estimate the proportion of voters who will support a particular cand

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

Effectiveness of a New Vaccine

A pharmaceutical company is testing a new vaccine. In a clinical trial, out of 1500 participants, 13

Factory Quality Control Analysis

In a factory, quality control is carried out by inspecting a sample of items. Out of 800 items inspe

Health Intervention Program Effectiveness

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

Public Health: Smoking Rates by Region

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

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

Restaurant Hygiene Survey Analysis

A local health department collected data on restaurant hygiene. In a simple random sample of 100 res

Retail Customer Satisfaction Survey Design

A retail chain wants to compare customer satisfaction levels between two store locations. A survey a

Smoking Cessation Campaign Study

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

Social Media Usage and Political Opinions

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

Voter Initiatives on Environmental Policy

In a survey about a new environmental policy, 600 voters were asked whether they support the initiat

Analysis of Weekly Exercise Duration

A wellness program is designed to increase weekly exercise time. In a sample of 16 participants unde

Assessing Training Effects on Marathon Times

A sports scientist is evaluating the effect of a new training regimen on marathon finishing times. T

Comparing Average Heart Rates in Two Exercise Regimens

A fitness study compared the effects of two different exercise regimens on heart rate. Group 1 (n =

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

Comparison of Waiting Times: Urban vs. Rural Hospitals

A health researcher compares patient waiting times in emergency rooms between urban and rural hospit

Computer Downtime Analysis

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

Customer Satisfaction at Two Store Branches

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

Delivery Times: Standard vs. Express Shipping

A logistics company wants to compare the average delivery times for its two shipping methods. Data c

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

Dosage Effect on Symptom Reduction

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

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

Election Polling Power Analysis

In an election poll, a candidate claims to have 70% support. A critic believes the true support is 6

Fuel Efficiency Analysis

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

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

Impact of New Traffic Signals on Commute Times

A city installs new traffic signals at a busy intersection to improve traffic flow. Traffic engineer

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

Income Analysis for a Tech Company

A tech company wants to estimate the average annual bonus received by its employees. A survey of 22

Machine Downtime Analysis

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

Paired Analysis of Blood Glucose Levels Before and After a Meal

A nutritionist is interested in the effect of a meal on blood glucose levels. Ten participants have

Paired Data in Pre-Test and Post-Test Scores

A company runs a training program and measures employee performance before and after the program. Fo

Physical Activity and Cholesterol Levels

A nutritionist studies the impact of physical activity on cholesterol levels by comparing two groups

Precision in a Manufacturing Process

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

Public Transportation Use and Environmental Awareness

A survey examines whether public transportation usage is related to environmental concern. Participa

Quality Control in Food Packaging

A snack food company advertises that its bags contain 305 grams of product. To ensure quality, a ran

Quality Control in Production

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

Randomized Field Experiment on Stress Reduction

A research team is interested in determining whether a mindfulness training program reduces stress l

Response Time in a Virtual Reality Task

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

Role of Random Sampling in Simulation Studies

A statistician conducts a simulation study by drawing 1000 random samples of size n = 25 from a data

Simulation of Sampling Distribution for Mean Recovery Time

A hospital administrator runs a simulation study to assess the average recovery time (in days) after

Soil pH Variation

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

Study on Sleep Duration Effects

A research study investigates whether sleep duration affects employee productivity. In a random samp

Testing a New Drug's Effect on Cholesterol Levels

A pharmaceutical company claims that its new drug lowers LDL cholesterol levels. In a study of 12 pa

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

Weight Reduction Program Evaluation

A fitness center evaluates its new weight reduction program by measuring the weights of 15 participa

Animal Species Distribution in Habitats: Chi-Square Test

Researchers collected counts of three animal species (Deer, Rabbit, Fox) in two habitats. The counts

Blood Type Distribution: Goodness-of-Fit Test

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

Consumer Brand Preference Homogeneity Test

A consumer survey was conducted comparing brand preference for three competing brands (Brand X, Bran

Die Fairness: Goodness-of-Fit Test

A six-sided die was rolled 120 times with the following observed frequencies: Face 1: 10, Face 2: 20

Distribution of Housing Types in a City

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

FRQ 3: Voter Preferences by Age Group: A Homogeneity Test

A study categorizes voters into three age groups (Young, Middle, Older) and records whether they sup

FRQ 5: Health Supplement Side Effects

A double-blind clinical trial is conducted to compare a new health supplement with a placebo. Partic

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 12: Employee Training Program and Job Promotion

A company is investigating the effectiveness of its training program on job promotions. The collecte

Genetic Trait Distribution Goodness-of-Fit

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

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

Goodness-of-Fit Test for Dice Fairness

A six-sided die is suspected of being biased. In an experiment of 120 rolls, the observed frequencie

Goodness-of-Fit Test for Web Traffic Sources

A website manager expects that web traffic comes from four sources with the following proportions: D

Homogeneity in Voter Turnout Among Demographic Groups

Exit polls in three different cities recorded voter turnout (Voted, Did Not Vote). Use the data to t

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

Marketing Strategy Effectiveness

A company wants to assess if customer responses vary by the type of advertisement. Three ad types (O

Product Defect Rates – Chi-Square Goodness-of-Fit

A quality control engineer hypothesizes that defects in a product occur with equal probability among

Race Participation in Marathon

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

Satisfaction Survey Among Product Users: Chi-Square Test for Independence

A company wants to investigate whether customer satisfaction is independent of product type. A surve

Shopping Behavior: Online vs. In-store by Age Group

Researchers want to examine if shopping mode (Online vs. In-store) is related to age group. The surv

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 and Age: Test for Independence

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

Social Media Usage Among Age Groups: Independence Test

A survey of 250 social media users collected data on their primary platform (Facebook, Instagram, Tw

Socioeconomic Status and Book Reading Frequency: Independence Test

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

Species Distribution in a Wildlife Reserve

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

Teaching Methods Effectiveness: Homogeneity Test

An educational study compares the effectiveness of three teaching methods (Method 1, Method 2, Metho

Voter Turnout by Age Group Homogeneity Test

A political scientist wants to compare voter turnout (Yes, No) across three age groups: Young, Middl

Weather Patterns and Energy Consumption

A utility company is interested in whether weather conditions are associated with high or low energy

Workplace Safety Compliance

A company records the safety compliance of employees in two departments: Manufacturing and Administr

Coffee Consumption and Alertness

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

Coffee Consumption and Reaction Time Study

A study was conducted to examine the relationship between the number of cups of coffee consumed by c

Customer Satisfaction and Wait Times

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

Dosage of Medication and Blood Pressure Reduction

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

Effect of Experience on Salary

A company collected data on employees' years of professional experience (x, in years) and their annu

Effect of Study Habits on Exam Scores

Researchers are studying whether the number of extra study sessions (x) is related to improvement in

Effects of Weather on Tourist Visits

The city tourism board collected data to study the relationship between daily high temperature (in °

Employee Experience and Salary

A human resources study examines the relationship between years of work experience ($$x$$) and annua

Energy Consumption and Temperature: Simulation Study

A data analyst is investigating the relationship between ambient temperature (in $$^\circ C$$) and h

Engine Size vs Highway Fuel Efficiency

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

Evaluating the Impact of Work Experience on Promotion Rate

An organizational study examines whether years of work experience (x) affect the promotion rate (y,

Exercise Duration and Weight Loss

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

Machine Calibration and Defect Rate

A manufacturing engineer is studying the impact of a machine's calibration setting ($$x$$) on its de

Manufacturing Quality Control

A quality control engineer investigates the relationship between machine operation time (in hours) a

Medication Dosage and Blood Pressure Reduction

A study investigates the effect of medication dosage (x, in mg) on blood pressure reduction (y, in m

Multiple Regression: Interpreting Slope in Presence of Collinearity

In a study using multiple regression to predict housing prices, several predictors (e.g., square foo

Predicting Blood Pressure Based on Age

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

Sleep Hours and Reaction Time

A psychology experiment studies the effect of sleep duration (in hours) on reaction time (in millise

Social Media Engagement and Online Sales

An e-commerce company investigates the relationship between daily social media engagement (measured

Speed and Fuel Efficiency

A study examines the relationship between vehicle speed ($$x$$, in mph) and fuel efficiency ($$y$$,

Temperature and Electricity Consumption

A power company studies the relationship between daily average temperature (in °C) and electricity c

Temperature and Ice Cream Truck Sales

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

Temperature Effect on Ice Cream Sales

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

Weekly Internet Hours vs Exam Score Improvement

An education researcher collected data on the number of weekly hours students spent on the internet