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College of Business - Computer Information Systems and Business Analytics

 


 


COB 191 Learning Objectives

COB 191 BUSINESS AND ECONOMIC STATISTICS 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.
    • 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.
    • 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.
    • 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.
    • 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.
    • 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)
    • 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.)
    • 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.
    • Analyze the Credibility of Claims Made About Populations
      • Explain both the logic underlying hypothesis testing and the limitations on the conclusions that it permits.
      • Identify the appropriate null and alternative hypotheses for a hypothesis test.
      • Conduct a hypothesis test for one mean, either by the p-value approach or the critical region approach. The test may be one-tailed or two-tailed. Excel may be used.
      • Conduct a hypothesis test for one proportion, either by the p-value approach or the critical region approach. The test may be one-tailed or two-tailed. Excel may be used.
      • Apply the concepts of Type I and Type II error to a problem.  Explain the inverse relationship between the probabilities of the two types of error.
    • Analyze the Credibility of Claims Made About Pairs of Populations
      • Conduct a hypothesis test of the difference between two population means.