##### COB 191 BUSINESS ANALYTICS LEARNING OBJECTIVES

Upon completing COB 191, students should be able to do the following:

1. Collect Data
• Differentiate between a population and a sample.
• Differentiate between parameters and statistics.
• Identify data as either qualitative (categorical) or quantitative (numeric).
• Identify quantitative data as either discrete or continuous.
• Identify level of measurement of data: nominal, ordinal, interval or ratio.
• Briefly describe common sampling techniques: simple random, systematic, stratified, cluster, and nonprobabilistic.
• Briefly describe common errors in sampling: coverage (frame), nonresponse, sampling, and measurement.
• Use a random number table to select a random sample from a population list.
• Enter a data file into Excel.
2. Present Data
• Use Excel to present data in tables: frequency, relative frequency, cumulative frequency, cumulatative relative frequency and cross tabulation. Interpret data presented in such tables.
• Use Excel to present qualitative data or grouped quantitative data with charts: bar, pie, Pareto. Interpret data presented in such charts.
• Use Excel to present quantitative data with charts: stem and leaf plot, histogram, frequency polygon, box and whisker plot , scatter plot, ogive. Interpret data presented in such charts.
3. Summarize Data Numerically
• For a sample or a population, calculate and explain the measures of central tendency (mean, median and mode) and their relative merits.
• For a sample or a population, calculate and explain the measures of dispersion (standard deviation, variance, range, and coefficient of variation) and the relative merits of each.
• Recognize outliers and their impact on the various measures of central tendency and dispersion.
• Interpret percentiles, quartiles, IQR and the coefficient of correlation (Pearson's r).
• Recognize skewed and symmetric distributions
• Use Excel to obtain descriptive statistics: central tendency, dispersion, and correlation (Pearson's r).
• Apply the empirical rule to interpret standard deviation for approximately normal distributions.
4. Work with Probabilities
• Apply fundamental concepts of probability: experiment, trial, probability, random variable and sample space.
• Identify simple and compound events, including union ("or") and intersection ("and", joint events).
• Identify mutually exclusive events, independent events, and complementary events.
5. Use the Binomial Distributions (and Other Discrete Distributions)
• Articulate the relationship between a discrete probability distribution and a relative frequency distribution.
• Recognize a word problem that requires the binomial distribution. Compute the mean and standard deviation of this distribution. Identify the quantity required to answer the question.
• Calculate binomial probabilities using Excel: P(X=n), P(X < n), P( X > m), and P(m < X < n)
• Recognize a word problem that requires the Poisson distribution. Calculate P(X = n) using Excel.
6. Use the Normal Distribution (and Other Continuous Distributions)
• Articulate the relationship between area and probability for a continuous probability distribution.
• Relate measures of central tendency to the (graph of the) probability distribution. Also relate the measures of dispersion to this graph.
• Recognize normal distributions and their key properties: shape, range, mean, standard deviation.
• Identify the standard normal distribution. Recognize that if X is distributed as a standard normal, then X = z.
• Calculate and interpret z scores for values of normally distributed random variables, given mu and sigma.
• Articulate how knowing P(X < a) for all values a allows the calculation of P(a < X < b) for any values of the constants a and b. (Here, X is a continuous variable.)
• Compute P(a < X < b), P(X > a), and P(X < b) for a normally distributed variable X (using Excel)
7. Make Predictions about Samples Based on the Underlying Population
• Describe the "thought experiment"resulting in the sampling distribution of a statistic.
• Calculate the mean (expected value) and the standard error of the sampling distribution of the mean
• Apply the Central Limit Theorem to approximate the sampling distribution of the mean.
• Construct the sampling distribution of the proportion, given the population proportion p.
• Compute the probability that a sufficiently large sample drawn from a given population will have its mean in a specified range (using Excel).
• Using Excel, compute the probability that the proportion of successes in a series of Bernoulli trials falls in a specified range. (This assumes that the chance of each trial being a success is known and fixed.)
8. Make Predictions about the Underlying Population Based on a Sample
• Define a point estimate and explain the meaning of the term "unbiased estimator (of a population parameter)"
• Define the term "interval estimate", and clearly articulate the meaning of expressions such as "the 90% confidence interval for the mean is 10.6 to 11.5".
• Work with the t-distribution, finding the t-value for a specified probability or a probability value for a given t. Determine appropriate degrees of freedom for the t. Ascertain whether a problem requires the use of the t.
• Calculate (using Excel) and clearly state the confidence interval for the population mean, both when sigma is known and unknown.
• Calculate (using Excel) and clearly state the confidence interval for the population proportion.
• Determine appropriate sample size for estimating the population mean, given an approximation of sigma and a target margin of error.