## COB 191 Learning Objectives

### COB 191 BUSINESS AND ECONOMIC STATISTICS LEARNING OBJECTIVES

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

- 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.