SHS Staff Pages: Grabowski, Mary

Probability & Statistics Syllabus

by Carol Braun

September 20, 2005

STATISTICS AND PROBABILITY

PURPOSE

Today, more than ever, statistics plays a very important role in our lives. This course has been designed to provide the student with a comprehensive treatment of introductory statistics and probability in such areas as sociology, business, ecology, economics, education, medicine, psychology, and mathematics. Students in these fields must frequently demonstrate a knowledge of the language and methods of statistics. Methodology and applications have been integrated throughout the course.

In Chapter 1, the student will discuss the nature of statistics. They will also identify the two major areas of statistics ( descriptive and inferential ). The student will also distinguish between a sample and population.

As indicated in Chapter 1, descriptive statistics involves collecting data and tabulating them in a meaningful way. In this chapter we indicated how to organize the data and then present the results graphically. The student will work with frequency distribution. and be able to graph the distribution in the form of a histogram, circle graph, frequency polygons, bar graphs and stem-leaf.

In Chapter 3 we discuss arithmetic methods of summarizing data. We will find the measures of central tendency (mean, median, and mode). We will also find the measures of variation (range, standard deviation, variance, and average variance). The student will analyze percentiles and z-scores.

In Chapter 4 the student will studied the basic ideas of probability that will enable us to evaluate the likelihood that our statistical inferences are correct. The student will find the probability that a particular thing will happening. The student will learn how to find permutations and combinations.

Although probability was defined in the last chapter, nevertheless, we need rules for determining probabilities of events involving "and" or events involving "or". Also, we may be interested in determining probabilities given that other events have occurred. In Chapter 5 we analyze various rules of probability.

As random variables and probability distributions play a key role in our later studies of statistical inferences, in Chapter 6 we analyze the nature of and applications involving discrete random variables and their associated probability distributions.

In Chapter 7, we discuss in detail a probability distribution that is bell shaped and is called the normal distribution. The normal distribution can be used to calculate probabilities. The student will apply the normal distribution to many different situations. This is accomplished by converting to z-scores and using the standard normal distribution.

In Chapter 8 we discuss several sampling techniques. We discuss how to make good questions for a survey and how to get a random sample. Some of the methods is cluster, random, stratified and survey. The student will find the sample mean and apply it to problems. We also consider an important theorem - Central Theorem- which gives us some very significant information about the sampling distribution of the mean. These ideas will be used extensively in later chapters when we discuss statistical inferences.

In Chapter 9 we indicate how sample statistics can be used to provide estimates for the mean of a population, the proportion of a population that has a particular attribute, and the standard deviation of the population. Since such estimates are necessarily subject to sampling error, we can provide information about the accuracy of such estimates by setting up confidence intervals and by selecting a sample of the appropriate size.

Chapter 10 we indicate how statistics can be used to make decisions ab out certain assumptions called hypotheses. Statistical inferences of this type are called hypotheses tests. We will analyze procedures for testing hypotheses regarding means, differences between means, and proportions, The appropriate procedure will vary and depend on whether we have a small or large sample size.

Chapter 11 deals with procedures that can be used to determine when a relationship exists between variables and also to find an equation expressing such a relationship. Thus, we will study correlation and regression.

In Chapter 12 we apply hypothesis-testing procedures to determine whether two characteristics or a population as given in a contingency table are statistically independent or whether observed data follow some pattern. This is referred to as goodness of fit. The chi-square distribution plays a key role in such analyses.

In Chapter 13 we test hypotheses about several means, The ANOVA techniques to be discussed allow us to test the null hypothesis that all sample means are equal against the alternate hypothesis that at least one mean value is different.

STANDARDS

At the end of their junior year, every student is to have taken and pass the state standards. Most of the students will have taken all the test by the time they are in this course.

The first semester we will review the strands 1, 2, 3, and 4. The students that have not pass the tests in these standards will take the tests during the study time. I will work with the student for a couple days on the type of problems and then take the test. We may have to take the test several times.

Second semester we will take the test son strand 5 and 6. Strand 5 is the Probability .

STUDENT GRADING

Homework and quizzes will be worth 15% . The standard tests will be worth 10%. Tests will be worth 75%. Each quarter will be given a percentage value, they will be added along with a semester test to find your grade. The semester test will be comprehensive and is worth 10% of your total grade. The way it works is that the maximum value for one quarter is 45% and the other quarter is 45% and the semester is 10%. So it works out to be .45 + .45 + .10 = 1.00 X 100 = SEMESTER GRADE.

MAKE UP WORK

You will have till the day of the test in that chapter to make up work for any absence. After the test the work will not be graded.

CLASSROOM RULES

Students are to come to class prepared which includes, bring all materials and being on time. Students at all times are to be respectful of the teacher and other students in the room. Work is to be done in pencil. If work is not done in pencil, 15 points will be taken off your grade. If you need a pencil, you may rent of buy one. If you are late to class, bring a pass. If you do not have a pass it is ten minutes after school. During study time , you may go to the bathroom or get a drink. If you do not follow school rules you will be given a detention. Detentions will vary depending on the negative action and will be at the discretion of the teacher.

ABSENCES

The school allows for 10 missed days during the semester. If you go over this amount you will need to ge signed permission from the teacher if you wish to receive credit.