Statistics: 1001 Practice Problems For Dummies (+ Free Online Practice)

Book Preface

One thousand and one practice problems for statistics! That’s probably more than a pro-fessor would assign you in one semester (we hope!). And it’s more than you’d ever want to tackle in one sitting (and we don’t recommend you try). So why so many practice problems, and why this book?
Many textbooks are pretty thin on exercises, and even those that do contain a fair number of problems can’t focus on all aspects of each topic. With so many problems available in this book, you get to choose how many problems you want to work on. And the way these problems are organized helps you quickly find and dig into problems on particular topics you need to study at the time. Whether you’re into the normal distribution, hypothesis tests, the slope of a regression line, or histograms, it’s all here and easy to find.
Then there’s the entertainment factor. What better way to draw a crowd than to invite people over for a statistics practice problems marathon!

What You’ll Find

This book contains 1,001 statistics problems divided into 17 chapters, organized by the major statistical topics in a first-semester introductory course. The problems basically take on three levels:

» Statistical literacy: Understanding the basic concepts of the topic, including terms and notation
» Reasoning: Applying the ideas within a context
» Thinking: Putting ideas and concepts together to solve more difficult problems

In addition to providing plenty of problems to work on in each chapter, this book also provides worked-out solutions with detailed explanations, so you aren’t left high and dry if you get a wrong answer. So you can rest assured that when you work for 30 minutes on a problem, get an answer of 1.25, and go to the back of the book to see that the correct answer is actually 1,218.31, you’ll find a detailed explanation to help you figure out what went wrong with your calculations.

How This Workbook Is Organized

This book is divided into two main parts: the questions and the answers.

Part 1: The Questions
The questions in this book center on the following areas:

» Descriptive statistics and graphs: After you collect and review data, your first job is to make sense of it. The way to do that is two-fold: (1) Organize the data in a visual manner so you can see it and (2) crank out some numbers that describe it in a basic way.
» Random variables: A random variable is a characteristic of interest that varies in a random fashion. Each type of random variable has its own pattern in which the data falls (or is expected to fall), along with its own mean and standard deviation for the data. The pattern of a random variable is called its distribution.
The random variables in this book include the binomial, the normal (or Z), and the t. For each ran-dom variable, you practice identifying its characteristics, seeing what its pattern (distribution) looks like, determining its mean and standard deviation, and, most commonly, finding probabili-ties and percentiles for it.
» Inference: This term can seem complex (and word on the street says it is), but inference basically just means taking the information from your data (your sample) and using it to draw conclusions about the group you’re interested in (your population).
The two basic types of statistical inferences are confidence intervals and hypothesis testing:
• You use confidence intervals when you want to make an estimate regarding the population — for example, “What percentage of all kindergarteners in the United States are obese?”
• You use a hypothesis test when someone has a supposed value regarding the population, and you’re putting it to the test. For example, a researcher claims that 14 percent of today’s kindergarteners are obese, but you question whether it’s really that high.
» The underpinnings needed for both types of inference are margin of error, standard error, sampling distributions, and the central limit theorem. They all play a major role in statistics and can be somewhat complex, so make sure you spend time on these elements as a backdrop for confidence intervals and hypothesis tests.
» Relationships: One of the most important and common uses of statistics is to look for relation-ships between two random variables. If variables are categorical (such as gender), you explore relationships by using two-way tables containing rows and columns, and you examine relation-ships by looking at and comparing percentages among and within groups. If both variables are numerical, you explore relationships graphically by using scatter plots, quantify them by using correlation, and use them to make predictions (one variable predicting the other) by using regression. Studying relationships helps you get at the essence of how statistics is applied in the real world.
» Surveys: Before you analyze data in all the ways mentioned in this list, you have to collect the data. Surveys are one of the most common means of data collection; the main ideas of surveys to address with practice are planning a survey, selecting a representative sample of individuals to survey, and carrying out the survey properly. The main goal in all of these areas is to avoid bias (systematic favoritism). Many types of bias exist, and in this book, you practice identifying and seeing ways to minimize them.

Part 2: The Answers
This part provides detailed answers to every question in this book. You see how to set up and work through each problem and how to interpret the answer.