By the end of this lesson, you should be able to:

- Explain the course policies
- Access course resources (course outline, lesson schedule, preparation activities, reading quizzes, homework assignments, assessments, etc.)
- Communicate with the instructor and group members
- Access statistical analysis software tools for class quizzes, assignments, and exams
- Apply principles of the gospel of Jesus Christ in this class
- Apply the three rules of probability for different probability scenarios

In this course, you will explore important connections between the academic discipline of Statistics and the world around us. By pondering these ideas, your understanding of statistics will increase, as will your knowledge and testimony of the restored Gospel of Jesus Christ. In addition, that which you learn in this course will increase your ability to serve others as a disciple of Jesus Christ and help build Zion.

If you have never taken an online class before, you are in for a new and exciting learning experience. This course uses some of the most advanced educational tools. These technologies will help you learn in an effective and efficient way, often allowing you to learn more than you would in a traditional Statistics class—and in less time. Although some of the learning activities will require you to work on your own, you will also be engaged in activities with other students and your instructor. Through your group interactions, you will have many opportunities to teach one another by sharing ideas and solving problems together.

This course has been designed to help you slowly build up a knowledge base of ideas and skills. Not all of these ideas and skills will come easily. It takes a lot of work and practice before some things will even start to make sense, so you should not be surprised to find that it may take you a little time to comprehend these ideas. Just be patient. Once you’re far enough into the course, the ideas will start to come together, and you will see how much progress you have really made. You will understand what this course is all about, and you will be glad you persisted in your efforts to learn.

As you thoughtfully prepare, teach one another, ponder/prove what you have learned, and as you humbly seek the guidance of the Holy Spirit, the Lord will bless you with a greater knowledge of His mercy and love. You will have the opportunity to increase your testimony of the Gospel of Jesus Christ. You will also learn about Statistics, more deeply and permanently than you would have otherwise.

This course covers the following topics as they are applied to Statistics: graphical representations of data, measures of center and spread; elementary probability; sampling distributions; correlation and regression; statistical inference involving means, proportions, and contingency tables.

In this course, we will:

- Summarize data numerically and graphically using spreadsheets
- Make decisions regarding situations with inherent randomness
- Apply probability distributions to investigate questions
- Employ confidence intervals in various situations
- Implement tests of diverse hypotheses
- Communicate the results of statistical analyses to relevant audiences

While you may not be tested on everything you learn in this course,
the instructor will be assessing your mastery of the **Course
Learning Outcomes**. The general types of assessments used to
measure these outcomes may include selected response tests such as
multiple-choice, true-false, matching, and fill-in-the-blank questions.
You may also be asked to complete essays or other writing assignments.
At times, the instructor may assess your performance of a skill, or the
instructor may assess products you create using particular skills. In
addition, the instructor may engage in personal communication with you
to determine how well you understand the course content.

You will experience much deeper learning if you follow the Five Principles of the BYU-Idaho Learning Model

**Exercise Faith**: Exercise faith in the Lord Jesus Christ as a principle of action and power.**Learn by the Holy Ghost**: Understand that true teaching is done by and with the Holy Ghost.**Lay Hold on the Word of God**: Lay hold of the word of God.**Act for Themselves**: Act for yourself and accept responsibility for learning and teaching.**Love, Serve, and Teach One Another**: Love, serve, and teach other students in your classes.

You will learn more in less time if you follow the Three Process Steps of the BYU-Idaho Learning Model

**Prepare**: This involves (a) spiritual preparation, (b) individual preparation, and (c) group preparation.**Teach One Another**: You should (a) be on time, (b) pray together, and (c) actively engage with other students.**Ponder/Prove**: You should (a) ponder what you have learned, (b) record your learning, and (c) pursue unanswered questions and discuss what you learn with others.

If you feel confused or have questions about anything in the lesson, take immediate action (Exercise Faith; Act for Themselves) and talk with your classmates, the teaching assistant, or the instructor (Love, Serve, and Teach One Another).

**Teach One Another**

At BYU-Idaho, an “A” student will demonstrate “diligent application of Learning Model principles, including initiative in serving other students” (BYU-Idaho Catalog). In this class, you will have the opportunity to work with other students.

Doctrine and Covenants 84:106 states, “And if any man among you be strong in the Spirit, let him take with him him that is weak, that he may be edified in all meekness, that he may become strong also.” In the spirit of this revelation, you will have the opportunity to help others in the class when you have developed an understanding of a principle. Likewise, you will be able to receive help from others (peers, tutors, TA, and your instructor) when you are still working to understand concepts.

This course represents a collaborative effort between faculty, TA’s, tutors, students and the Lord. You are encouraged to seek the help from seen and unseen resources as you grapple with the principles of Statistics.

In a spirit of love and service, please reach out to others. You are not graded on a curve. If someone else does well, it does not affect you adversely. Research has shown that students who help other students to understand the material gain a much deeper grasp on the concepts of the course. Please take opportunities to help your peers succeed.

The structure of this course is based on scientific research on student learning and retention. The activities, structure, pace, and repetition are all grounded in modern educational theories and practices. This course has been designed with you, the student, in mind. This course consists of 24 lessons. They are presented in a topical order in which concepts and skills learned in the earlier lessons provide the requisite knowledge to succeed in later lessons. If the general order of the lessons doesn’t make sense at first, don’t worry. It will all come together in the end, and you’ll see the reasoning behind why the lessons have been presented in this particular order. Your main goal as a student will be to complete all of the learning activities within each lesson by their due dates every week. These activities follow a consistent weekly schedule, and it will be up to you to make sure that you keep on pace with all your assignments. These weekly activities may include the following: Reading assigned texts and/or viewing videos. Taking quizzes. Participating in group discussions with other class members using WhatsApp. For many of these activities, the due dates will fall on the same time each week. This will make it easier for you to plan out your weekly study schedule. However, there may be a need to make adjustments to the schedule from time to time. If in doubt, refer to the due dates your instructor has posted in I-Learn. And now for a word of warning. If you start to fall behind, please contact your instructor immediately to discuss your questions, concerns, and strategies to improve in the course. This is a rigorous course with a lot of subject matter to cover, and it can be extremely difficult to recover if you fall too far behind in your work. So, please make every effort to study on a regular basis and get your work turned in on time.

The lessons in this course have a similar structure and contain similar basic elements. A typical week consists of four lessons.

The learning activities fully integrate the BYU-Idaho Learning model. They contain a mixture of preparation activities, teach-one-another activities, and ponder-and-prove activities. You will need to complete these activities in the order in which they are listed.

Each lesson begins with a reading assignment. These readings, as well
as helpful instruction videos, are provided in this online textbook. Be
sure to answer the questions in the textbook, since these are an
important part of the learning process. Use the Preparation and Practice
worksheet for each lesson as a study guide to help you keep organized
notes on the content and to practice solving problems from the lesson.
Taking good notes is an important part of being prepared for future
quizzes and exams. **After completing the Preparation and Practice
worksheet, you will compare your responses with those in the answer key
to check your understanding of the content and practice
problems.**

After completing your individual preparation for each lesson, you will then work with your group in Whatsapp to answer any lingering questions until everyone in your group understands the lesson.

After you have completed your individual and group preparations, you may begin the lesson quiz. You will have three attempts to complete the quiz. Each attempt will have different questions but the same concepts will be tested. After your first attempt, seek help from your group to gain a better understanding of the problems that you missed. Then take the quiz again. On the second and third attempts, you can get help from your group or a tutor. This quiz is a tool to help you and your instructor gauge your progress.

You can use the calendar feature in I-learn to see the schedule of lessons. A typical week consists of four lessons.

There are several benefits of this consistent lesson structure.
First, it helps you establish a regular schedule for studying and
participating in class activities. Second, it helps you learn more in
less time. By the third or fourth lesson, you will find that it takes
you less time to navigate through the course and complete certain
activities and you will know what you need to do to succeed. Third, it
gives you an opportunity to develop discipleship and leadership by
teaching other students on a regular basis **through
WhatsApp**. Finally, the lesson structure makes it easier for you
to give feedback to the instructor so that future lessons may be
improved. This is an important part of the “teach one another” concept
in the BYU-Idaho Learning Model. By giving feedback on what does and
does not work for you in each lesson, you help other BYU-Idaho students
get more out of the class. So, as you go through each lesson, feel free
to make notes about the things that worked well for you, as well as the
things that could be improved. Include these ideas in the Lesson
Evaluation Survey. Your efforts to provide feedback to the instructor
will not only help improve the course, but by taking the time to think
about these things, you will become a better teacher yourself.

This course has been designed with the student in mind. Every effort has been made to provide a high quality experience at the lowest possible cost.

To keep costs as low as possible for students and their families, no textbook is required for this class. The readings for this course are provided in this online textbook.

**Computer Equipment**

You will need: - A laptop - Access to Microsoft Excel 2016 or later

**Textbook**

The readings for this course will all be presented in this online
textbook. Take some time to explore it. You can click on **Math
221** in the navigation menu (upper left part of the page) to get
to the main directory.

We will use WhatsApp for students and teachers to connect with each other. Once you get used to its functionality, it will be a great tool for learning.

**Peer Support**

Your experience in this course will be enhanced as you work with other students to learn and grow together.

**Help Desk**

The BYU-Idaho Help Desk has been established to help students with technological problems related to approved course software. You can access the Help Desk at any time. You can either contact BYU-Idaho Technology Support or get general help from the Help Desk. When you have technical problems with I-Learn, you should first try contacting Technology Support before you contact your instructor. They are connected with the IT support staff who can resolve problems with I-Learn. Please take 5 minutes now to look at the Help Desk web page. That way, if a problem does arise later on in the course, you will know where to go for help.

**Tutoring Center**

The BYU-Idaho Study Skills/Tutoring Center is a powerful resource for students who would like a little extra help with a course. Please take 5 minutes to explore the Study Skills/Tutoring Center website.

**Faculty Support**

Your instructor is committed to your success. If you have any needs or concerns, please contact your instructor for help. If you feel yourself getting behind or struggling, talk to your teacher right away. If caught in time, a small problem can be addressed quickly before it grows.

There are three basic things you must do to succeed in this course.

- Do the work.
- Stay on schedule.
- Follow the Honor Code.

If you do these three things, you will not only get a passing grade for the course, but you will have an excellent educational experience. Here’s why.

This is a rigorous course. To get a passing grade, you will have to put forth a good deal of effort to complete all of the assignments. When you see a time estimate next to a learning activity, that is the approximate amount of time it will take IF you are focused on the assignment and IF you are not allowing yourself to be distracted by other things. You will have a very difficult time completing these assignments if you do them at the same time you watch TV, cook food, talk with your roommates or family members, and send text messages to your friends every three minutes. You must set aside sufficient time to do the work throughout the week (you can’t do it all in one night!). And you must find a place to do the work where you will not be distracted by anything (you can’t get it done with a cell phone call interrupting you every few minutes!). Then you must commit to focus your attention on the work and do your very best to complete it in the amount of time you have scheduled. If you do this, you will learn more in less time, and you will find the work much more pleasurable.

Once you have set up a regular study schedule, keep it. One of the biggest problems that students have with their courses is that they procrastinate doing the work. They put it off until they have so much work to do that they cannot figure out a way to get it all done before the due date arrives. In this course, you cannot do this and still expect to receive a passing grade. There are assignments that must be completed by specific days and times every week. If you put off doing the work until just before an assignment is due, you will find it much more difficult to concentrate on getting the work done. To succeed in this class, you will have to follow your regular study schedule every week to ensure that you do your best work and that it gets done on time.

Although there are several types of group learning activities in every lesson, this course requires a lot of individual study and work. In particular, most assignments involving a study guide and quiz are meant to be learning activities you complete on your own. If you decide to work with others to try find all the quiz answers without having to do all the assigned work, you are not only cheating yourself out of an education, you are cheating your way to a failing grade. There are other assignments throughout the course that will require you to recall information or use skills that you should have developed as you completed the learning activities. If you don’t do the work, and you try to cheat your way to higher quiz grades, you will hinder your ability to complete these other assignments. Most likely, you will fail those assignments. So, do yourself and others a favor–do not cheat on any assignments, no matter how tempting it might be. Instead, renew your commitment to follow the BYU-Idaho Honor Code, double your efforts to do the work, and follow your study schedule.

Clearly, if you want to succeed in this course, you need to figure out how you will do the work and how you will stay on schedule. Doing this will help you avoid situations in which you might be tempted to violate the Honor Code and cheat. Such situations can arise quicker in the semester than you might think. So, it is important for you to start making a plan for success right away. Take time now to write your own plan for success. This plan should include a weekly study schedule and a general list of things you think you will need to do each week to get the work done. Be prepared to discuss this plan with your study group and with the instructor.

- Write your own Plan for Success in this course. The plan should include a weekly study schedule and a general list of things you think you will need to do each week to get the work done.

Probability is a way of numerically quantifying how likely an event is to happen or not happen. The following historical account demonstrates this idea and shows how fractions (like 1/2 or 3/4) or percentages (like 50% or 75%) can be used to represent probabilities.

On August 3, 1492, Columbus set sail from Spain for his intended destination: the Indies (Caso, Adolph 1990). He was on the Santa Maria, which had a crew of approximately 41 men (“Cristobal colon” 1991; “Christopher Columbus”). Several other men were aboard the Nina and the Pinta (“Cristobal colon” 1991). On October 12, he landed on an island in the Bahamas he called San Salvador.

The return trip was not without challenges. The Santa Maria ran aground on Christmas Day, 1492, and was abandoned on the island we now call Hispaniola (home to Haiti and the Dominican Republic). Following this incident, Columbus sailed for Spain. Severe storms made the journey difficult. A particularly bad storm on February 14, 1493 made the crew fear for their lives. By morning, the storm was even worse!

Recognizing his dependence upon God, Columbus ordered that a pilgrimage should be made to a particular shrine upon their safe arrival in Spain. He decided that they would use random chance to determine who would make the pilgrimage. They took one chick pea for each man on board. A knife was used to mark one of the chick peas with a cross. The chick peas were placed in a hat and shaken up. Each man was to draw a chick pea, and the one who had the cross would make the pilgrimage.

“The first who put in his hand was [Columbus,] and he drew out the bean with a cross, so the lot fell on him; and he was bound to go on the pilgrimage and fulfil the vow” (Caso, Adolph 1990).

Answer the following questions:

- Remember, there were 41 men aboard his ship. What is the probability that Columbus would draw out the marked chick pea? Express your answer as a fraction, and then convert it to a decimal.

- Based on your answer to the previous question, how likely is it that Columbus would draw out the marked chick pea?

**A Second Drawing**

Columbus’ promise to make the
pilgrimage did not stop the storm. It was determined that there should
be a pilgrimage to another site they held sacred. Again, chick peas
representing each member of the crew were placed in a hat and shaken up.
The lot fell on a sailor…named Pedro de Villa (Caso, Adolph 1990).

Answer the following questions:

- What is the probability that Columbus would not draw out the marked chick pea? Express your answer as a fraction, and then covert it to a decimal?

- Based on your answer to the previous question, how likely is it that Columbus would not draw out the marked chick pea?

- In this second drawing, either Columbus would draw out the marked chick pea, or he would not. Add the probability that Columbus would draw out the marked chick pea and the probability that he would not draw out the marked chick pea. What is the value of this sum?

**Additional Drawings**

After the drawing in which Pedro de Villa was chosen to make a pilgrimage, two additional drawings were held. In both cases, Columbus drew out the marked chick pea (Caso, Adolph 1990). In all, Christopher Columbus drew the marked chick pea in three of the four drawings. It can be shown that the probability that this would occur due to chance is very small: 0.0000566. (Show/Hide Solution)

To put some perspective on this, a high school athlete in the United States is over 26 times more likely to play professional sports than Columbus was to draw the three marked peas! (Fields, Mike 2008) Consider how you might explain the occurrence of this extremely unlikely event. (While no response is required of you right now, this kind of question will be very important later, so take a little time to ponder it.) In fact, it is worth restating the question, “How might you explain the occurrence of this extremely unlikely event?”

Now, take a moment to practice what you have read by answering the following questions.

Answer the following questions:

- If a fair, six-sided die* is rolled, what is the probability of rolling a 6?

- If a fair, six-sided die is rolled, what is the probability of not rolling a 6?

- When a die is rolled, what is the sum of the probability of rolling a 6 and the probability of not rolling a six?

- In general, if we know the probability that a particular outcome will occur, how could we calculate the probability that it will not occur?

\(*\)*Note: The word “die” is the
singular form of the word “dice.” When we refer to a die, we are talking
about a fair, six-sided die.*

You may already have a good understanding of the basics of probability. It is worth noting that there is a special notation used to denote probabilities. The probability that an event, \(x\), will occur is written \(P(x)\) and pronounced as “probability-of-event-x.” As an example, the probability that you will roll a 6 on a fair six-sided die can be written as

\[ P\text{(Roll a "six" on a fair six-sided die)}= \frac{1}{6} = \frac{\text{number of sides that show a "six"}}{\text{total number of sides on the die}} \]

Probabilities follow patterns, called **probability
distributions,** or just *distributions*, for short. There
are three rules that a probability distribution must follow. Answer the
following questions to explore what these three rules might be.

Answer the following questions:

- As an answer to a homework problem, a student reported, The probability of finding life on Mars is -0.35. What is wrong with this statement?

- A student in an introductory statistics class wrote the following statement on an exam: The probability that the event will occur is 1.25 (i.e. 125%). What is wrong with this statement?

- A student estimated that the probability that he would finish his homework is 0.45 (i.e., 45%), and the probability that he would not finish his homework is 0.35 (i.e., 35%). What is wrong with this student’s statement?

In this course we are interested in experiments where the outcomes of
the experiment are uncertain, yet they follow a pattern or
*probabilitiy distribution.* As you read in the above questions
and answers, these probability distributions follow three rules.

**The three rules of probability are:**

**Rule 1**: The probability of an event \(X\) is a number between 0 and 1.

\[0 \leq P(X) \leq 1\]

**Rule 2**: If you list all the outcomes of an experiment (such as rolling a die) the probability that one of these outcomes will occur is 1. In other words, the sum of the probabilities of all the possible outcomes of any experiment is 1.

\[\sum P(X) = 1\]

**Rule 3**: (Complement Rule) The probability that an event \(X\) will not occur is 1 minus the probability that it will occur.

\[P(\text{not}~X) = 1 - P(X)\]

You may have noticed that the Complement Rule is just a combination of the first two rules.

Answer the following questions:

- Which of the probability rules was violated by the statement in Question 10?

- Which of the probability rules was violated by the statement in Question 11?

- Which of the probability rules was violated by the statement in Question 12?

Informally, a distribution can be thought of as being “all the possible outcomes of an experiment and how often they occur.”

A BYU-Idaho student was overhead saying, “I went shopping and bought
some *random* items.” Did the person actually take a random
sample of the items at the store? Did they write all the items down and
randomly select the items for purchase? Of course not!

What did the student mean? That the items they bought seemed unrelated. When we consciously or subconsciously choose a sample, it is not random.

So, what does it mean to be random? When something is random, it is not just haphazard, with no pattern. A random process follows a very distinct pattern over time—the distribution of its outcomes. For example, if you roll a die thousands of times, about one-sixth of the time you will roll a four. This is a very clear pattern, or part of a pattern. The entire pattern (or, the entire distribution) is that each number on the die is rolled about one-sixth of the time.

But there’s something different about the patterns followed by random
processes than other kinds of patterns. Other kinds of patterns can be
very predictable, such as a color pattern of the red, yellow, blue, red,
yellow, blue, and so on. If you’re following this pattern and happen to
see yellow, you know the next color will be blue. By contrast, you never
know what you will get on the next roll of a six-sided die. You
*do* know that in the long run you will roll fours about
one-sixth of the time.

When something is random, we can be sure that it follows a long-term
pattern. This long-term pattern is called its *probability
distribution*. However, what makes “randomness” interesting is that
despite knowing the long-term pattern, or how often something will occur
over time, we still never know what the outcome of the *next*
experiment will be.

As with all the classes you take at BYU-Idaho, it is up to you to decide what you want to get out of this class. If you choose to approach the things you study in class with an open mind, if you prepare diligently and work hard to complete all the learning activities, and if you humbly seek the Lord’s help to understand the intellectual and spiritual truths discussed in this course and in other courses, you will have an outstanding educational experience that will be a blessing to you throughout your life. May you enjoy the journey this semester into statistics!

Remember…

In this class you will use the online textbook that has been written for you by your statistics teachers. All of the assignments and quizzes will be based on the readings, so study it well.

Most weeks will cover two lessons

By doing the work, staying on schedule, and living the Honor Code you

*will*succeed in this class!The three

**rules of probability**are:- A probability is a number between 0 and 1. \[0 \leq P(X) \leq 1\]
- If you list all the outcomes of a probability experiment (such as rolling a die) the probability that one of these outcomes will occur is 1. In other words, the sum of the probabilities in any probability is 1. \[\sum P(X) = 1\]
- The probability that an outcome will not occur is 1 minus the probability that it will occur. \[P(\text{not}~X) = 1 - P(X)\]

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