MATH201 Introduction to Statistical Methods I
                                                            Instructor: Dr. Carla C. Morris
                        TEXT: Statistics for Business and Economics by McClave, Benson, and Sincich (twelfth edition)

The following list of learning goals is designed to give you some guidance at what topics are important from the various sections we will cover from the book.  These goals are some of the key concepts that will be discussed for each section.  When you take exams in this course you must show me your work to earn full credit for a problem.  Correct answers with no work shown will be penalized. Partial credit will be given on problems therefore showing your work is vital to your grade and it also allows me to better determine where your weakness may be if you need assistance with any of the material.

There are several topics that we will discuss that are not included in your text.  Non- Graphing calculators are permitted and you will be allowed to copy any formulas appearing in the gray boxes to bring with you to exams.  However I will need to see that you understand how to calculate by hand some of the material that you will have a calculator or computer (Microsoft Excel) perform.

MATH201 CHAPTER 1 LEARNING GOALS (Statistics, Data, and Statistical Thinking)

• Understand the terms statistics, descriptive statistics, inferential statistics, population, sample, variable of interest, and measure of reliability.
• Be able to identify any of the four elements of a descriptive statistics problem
• Be able to identify any of the five elements of an inferential statistics problem
• Identify data as qualitative or quantitative
• Determine if qualitative data is on a nominal or ordinal scale
• Determine if quantitative data is on an interval or ratio scale
 

MATH201 CHAPTER 2 LEARNING GOALS (Methods for Describing Sets of Data)

*Your graphs should have a title that clearly identifies what the graph depicts, and axes should be labeled.  The title should include the sample size or total observations or money being depicted in your charts or graphs.   Your graphs should adhere to the general guidelines for the specific type of graph you plot that we will discuss during class.
• Be able to construct Pie charts and Bar charts for qualitative data
• Be able to construct Stem and Leaf Displays and Histograms for quantitative data
• Understand the difference between frequency, relative frequency, and relative frequency percentage
• Understand how to work with the summation operator
• Determine the measures of central tendency (mean, median, and mode)
• Determine the measures of variability or dispersion (range, variance, and standard deviation
• Be able to apply the formula for variance or its shortcut
• Be able to understand when to apply Chebyshev’s Rule or the Empirical Rule
• Work with samples or populations (Greek letters are often used in the population formulas
• Be able to interpret Z-scores for mound shaped distributions
 

MATH201 CHAPTER 3 LEARNING GOALS (Probability)
• Understand the terms, experiment, sample space, sample point (simple event), and event
• Calculate the probabilities of events
• Work with Venn Diagrams (unions, intersections, complements, etc.)
• Work with Combinations and Permutations
• Use the additive rule of probability
• Understand when events are mutually exclusive and what that means in terms of the additive rule of probability
• Work with conditional probabilities
• Determine whether two events are independent or dependent
 

MATH201 CHAPTER 4.1 – 4.4 LEARNING GOALS (Discrete Random Variables)
• Understand what a Random Variable (RV) is
• Understand when a rv is continuous or discrete
• Understand the requirements for the probability distribution of a discrete rv
• Determine the expected value (mean) and variance of a discrete random variable
• Work with the Binomial probability distribution, its characteristics and the corresponding table of probabilities
• Work with the Poisson random variable, its characteristics, and the corresponding table of probabilities
• Work with the Hypergeometric distribution (items selected without replacement)
• Work with the Geometric distribution (interest in the trial where the first success occurs)

MATH201 CHAPTER 4.5 - 4.8 LEARNING GOALS (Continuous Random Variables)


• Work with probability density functions (pdfs)
• Work with the Uniform distribution
• Work with the Normal distribution (Bell Curve)

  •  Find probabilities given z score between two values
  •  Find probabilities associated with raw data (you must convert to z scores and then use table)
    • • Determine whether a Binomial distribution can be approximated by a Normal distribution
    • Find probabilities when the Normal approximation for a Binomial distribution is appropriate (adjustment must be made for continuity)

    • Work with the Exponential distribution
     
    MATH 201 CHAPTER 5 LEARNING GOALS(Sampling Distributions)

    • Understand the definitions for parameter, sample statistic, sampling distribution, and point estimator
    • Determine if the mean or median of a sampling distribution is an unbiased estimator of the population mean
    • Use the Central Limit Theorem (CLT)
    • Remember now that sampling distributions will be used for remainder of the course that sample size is used in the calculations (watch for the subscript x bar on both mu and sigma)

    MATH201 CHAPTER 6 LEARNING GOALS (Inference Based on a Single Sample: Estimation with Confidence Intervals)
    • Understand the terms interval estimator, confidence level, and confidence coefficient
    • Determine the large sample confidence interval for a population mean
    • Notice all confidence intervals have a subscript of one half of alpha
    • Know how to determine the degrees of freedom for the t-statistic (df = n -1)
    • Determine the small sample confidence interval for a population mean
    • Determine the large sample confidence interval for a population proportion (make sure the assumptions hold before proceeding to calculate the interval)
    • Determine sample sizes (Round up to nearest whole number and if small sample size is calculated round all the way up to 30 so CLT is appropriate—Note this may differ in other books depending on the set of assumptions that are being used)
    • A sample is considered large if the sample size, n, is at least 30 and therefore a Z-statistic is used.  Proportions will also use the Z-statistic. When n is under 30 then a sample is considered small and a t-statistic with n – 1 degrees of freedom should be used.  In all cases the value of alpha is halved.  Chapter 6 follows the same guidelines for large and small samples but one must decide if a hypothesis test is one or two tailed.  All two tailed hypothesis tests will half the alpha value but one tailed tests such as less than or greater than will use alpha—Watch the subscripts in the formulas carefully)

    MATH201 CHAPTER 7 LEARNING GOALS (Inference Based on a Single Sample:Test of Hypothesis)
    • Understand the elements of a statistical hypothesis
    • Find the null hypothesis, alternative hypothesis, test statistic, rejection region, and state a general and specific conclusion at the specified value of alpha for each hypothesis test that you conduct
    • Conduct a large sample test of hypothesis about a population mean
    • The alternative hypothesis can be determined by investigating the question asked in a problem (The null hypothesis ids the status quo and the alternative is what you would like to prove is true)
    • Type II errors are committed when one accepts the null hypothesis when it was actually false.  We will try to avoid making this mistake by using the phrase “There is insufficient evidence at alpha = __ to reject the null hypothesis”
    • Remember to always state at what alpha level you are basing your conclusion because at a different value of alpha the conclusion could be different.
    • Remember the alternative hypothesis will be used to determine if a hypothesis test is one or two tailed
    • Determine the observed significance level for the test of hypothesis
    • Conduct a small sample test of hypothesis about a population mean
    • Conduct a large sample test of hypothesis about a population proportion
    • Remember that if the observed significance level is less than alpha then there is sufficient evidence to reject the null hypothesis
     

    MATH201 CHAPTER 8 LEARNING GOALS

    8.2 Comparing Two Population Means: Independent Sampling
    • Determine the properties of the sampling distribution of the difference in two sample means
    • Determine the large sample confidence interval for a difference in two means
    • Conduct a large sample hypothesis test for the difference in two means (Do is the hypothesized difference in the means which is usually zero unless otherwise specified within the problem)
    • Determine the small sample confidence interval for a difference in two means
    • Conduct a small sample hypothesis test for the difference in two means (Do is the hypothesized difference in the means which is usually zero unless otherwise specified within the problem)

    8.6 Comparing Two Population Variances: Independent Sampling
    • Work with the F statistic (tables in the back of the book)
    • Determine the correct degrees of freedom for both the numerator and denominator (one less than the sample size associated with the numerator and one less than the sample size associated with the denominator)
    • Always use F = larger variance/smaller variance (Note this means F is always at least one)