Statistics: 1,001 Practice Problems For Dummies

Book Preface

One thousand and one practice problems for statistics! That’s probably more than a professor 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 pro-vides 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 prob-lem, 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 random variable, you practice identifying its characteristics, seeing what its pattern (distribution) looks like, determining its mean and standard deviation, and, most commonly, finding probabilities and percentiles for it.
✓ Inference: This term can seem complex (and word on the street says it is), but infer-ence 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 pop-ulation, 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. All of them 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 relationships between two random variables. If variables are categorical (such as gender), you explore relationships by using two-way tables containing rows and col-umns, and you examine relationships by looking at and comparing percentages among and within groups. If both variables are numerical, you explore relationships graphi-cally by using scatter plots, quantify them by using correlation, and use them to make predictions (one variable predicting the other) by using regression. Studying relation-ships 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 col-lect 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 representa-tive 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 II: 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.

Beyond the Book

This book of 1,001 practice problems will keep you busy with pencil and paper for a while, but like the infomercials say, “Wait! There’s more!” Your book purchase also comes with a free, one-year subscription to all 1,001 practice problems online. Track your progress and view personalized reports that show where you need to study the most and what you’re pretty comfortable with.
What you’ll find online
The online practice that comes free with this book offers you the same 1,001 questions and answers that are available here, presented in a multiple-choice format. Multiple-choice ques-tions force you to zoom in on the details that can make or break your correct solution to the problem. Sometimes one of the possible wrong answers will catch you in the act of making a certain error. But that’s great because after you identify a particular error (often a common error that many others make as well), you’ll know not to fall into that trap again.
The beauty of the online problems is that you can customize your online practice — that is, you can select the types of problems and the number of problems you want to work on. The online program keeps track of your performance so you can focus on the areas where you need the biggest boost.
You can access this online tool by using a PIN code, as described in the next section. Keep in mind that you can create only one login with your PIN. Once the PIN is used, it’s no longer valid and is nontransferable. So you can’t share your PIN with others after you’ve estab-lished your login credentials. In other words, the problems are yours and only yours!