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PBL: STATISTICAL ANALYSIS
Competency: Descriptive Statistical Analyses
Tasks
1.
Define descriptive statistics.
2.
Identify the focus for descriptive analysis.
3.
Distinguish between descriptive statistics and inferential statistics.
4.
Describe a statistical package that facilitates computation and analysis.
5.
Describe the difference between statistical significance and practical significance.
6.
Apply a working knowledge of the vocabulary of modern statistics including conventional symbols, terminology, and
basic operations to communicate with others.
7.
Distinguish between predictions, guesstimates and statistics.
8.
Recognize different types of errors and the strengths and weaknesses of data.
9.
Calculate a mean, weighted mean, median and mode of a sample and population.
10. Describe the steps involved in choosing what statistical methods to use to conduct a data analysis.
11. Calculate the variance and standard deviation of a sample and population.
12. Use the empirical rule and Chebyshev’s theorem to predict the distribution of data values.
13. Use measure of relative position to identify outlier data values.
14. Describe types and sources of data.
15. Explain different ways of measuring data.
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PBL: STATISTICAL ANALYSIS
Competency: Organizing and Presenting Statistical Data
Tasks
1.
Explain the difference between data and information.
2.
Recognize the importance of visual displays in analyzing data.
3.
Describe the various ways to summarize, organize and present data.
4.
Establish specifications for data presentation.
5.
Classify data—quantitative or qualitative.
6.
Discuss the principles of properly presenting graphs.
7.
Develop tables and charts for categorical data.
8.
Develop tables and charts for numerical data.
9.
Describe the properties of central tendency, variation, and shape in numerical data.
10. Extract meaningful information from data sets.
11. Construct a stem and leaf display.
12. Graph a frequency distribution with a histogram.
13. Describe the usefulness of pie, bar, and line charts.
14. Define the process of coding data.
15. Create scatterplots.
16. Construct and interpret a boxplot.
17. Construct a frequency distribution.
18. Draw conclusions from histograms and frequency distributions.
19. Describe nominal data, ordinal data, interval data and ratio data.
20. Discuss the use of spreadsheet programs in entering and analyzing data.
21. Define a Pareto chart, histograms, pie charts, scatterplots and distribution shapes.
22. Calculate descriptive summary measures for a population.
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PBL: STATISTICAL ANALYSIS
Competency: Probability Distributions
Tasks
1.
Define probability distribution and its purpose.
2.
Examine the basic properties of probability.
3.
Define a random variable and probability distribution.
4.
Distinguish between classical, empirical and subjective probability.
5.
Discuss the role the terms variable and random variables play in probability distribution.
6.
Distinguish between cumulative probability distributions and uniform probability distribution.
7.
Define events, compound events and complementary events as they apply to basic probability.
8.
Demonstrate the intersection and union of simple events using a Venn diagram.
9.
Describe the distinction between independent and dependent events.
10. Describe and compute conditional probabilities.
11. Describe the characteristics of a binomial experiment.
12. Calculate the mean and standard deviation of a binomial distribution.
13. Compute probabilities for binomial distributed random variables.
14. Compute probabilities for normally distributed random variables.
15. Examine the properties of a normal probability distribution.
16. Use the standard normal table to calculate probabilities of a normal random variable.
17. Use the normal distribution as an approximation to the binomial distribution.
18. Use Bayes’ theorem to revise probabilities.
19. Use frequency distributions to calculate probability.
20. Calculate the mean and variance of a discrete probability distribution.
21. Describe the characteristics of a Poisson process.
22. Calculate probabilities using the Poisson equation.
23. Perform a goodness-of-fit test and a test of independence with the chi-square distribution.
24. Describe the characteristic and purpose of the chi-square distribution.
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PBL: STATISTICAL ANALYSIS
Competency: Sampling Techniques
Tasks
1.
Explain the concept of the sampling distribution.
2.
Distinguish between probability samples and non-probability samples.
3.
Describe each of the probability sampling methods: simple random, stratified, cluster, multistage and systematic
random sampling.
4.
Describe the four main methods of data collection: census, sample survey, experiment, and observational study.
5.
Identify the advantages and disadvantages of each method of data collection.
6.
Understand the influence of sample size on statistical significance and power.
7.
Use the normal distribution to compute probabilities for samples.
8.
Determine the sample size required to meet certain requirements for the standard deviation.
9.
Determine large-sample and small-sample confidence intervals for population means.
10.
Describe the importance of the Central Limit Theorem.
11.
Explain the reason for measuring a sample rather than the population.
12.
Define sampling errors and list some consequences for poor sampling techniques.
Competency: Linear Regression
Tasks
1.
Define linear regression and its use.
2.
Describe the best-fitting line or regression line.
3.
Determine the correlation and regression line for a set of ordered-pair data.
4.
Conduct and interpret the results of a simple regression analysis.
5.
Understand the similarities and differences between multiple regression analysis, analysis of variance, analysis of
covariance, and the general linear model.
6.
Distinguish between positive, negative, zero and undefined slopes.
7.
Distinguish between independent and dependent variables.
8.
Calculate a confidence interval for a regression line.
9.
Perform a hypothesis test on the regression line.
10. Explain the differences in simple versus multiple regression.
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PBL: STATISTICAL ANALYSIS
Competency: Confidence Integrity
Tasks
1.
Define confidence interval.
2.
Discuss the desirable properties for constructing confidence intervals.
3.
Describe the relationship of confidence interval with hypothesis testing.
4.
Construct and interpret confidence interval estimates for the mean and the proportion.
5.
Use confidence interval estimates in auditing.
6.
Calculate confidence intervals by using the t distributions.
7.
Identify misleading confidence intervals.
8.
Describe a process for calculating a confidence interval.
9.
Calculate the confidence interval for the mean with large and small samples.
10. Determine sample sizes to attain a specific margin of error.
11. Define a confidence level and a parameter.
12. Explain the effect of changing confidence levels and of changing sample size.
Competency: Hypothesis Testing
Tasks
1.
Discuss the steps of hypothesis testing.
2.
Describe the basic principles of hypothesis testing.
3.
Test hypotheses about a population mean or population proportion for both small samples and large samples.
4.
Determine what statistical test to use when.
5.
Explain the meaning of the null and alternative hypothesis.
6.
Define the terms “degrees of freedom,” margin of error, and statistical precision.
7.
Explain the assumptions of each hypothesis-testing procedure, how to evaluate them, and the consequences if they are
seriously violated.
8.
Explain how to avoid the pitfalls involved in hypothesis testing.
9.
Distinguish between a one-tail and a two-tail hypothesis test.
10. Control the probability of a Type I and Type II error.
11. Determine the boundaries for the rejection region for the hypothesis test.
12. State the conclusion of the hypothesis test.
13. Use the p-value to test a hypothesis.
14. Compare three or more population means using analysis of variance (ANOVA).
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PBL: STATISTICAL ANALYSIS
References:
Career Cluster Resources for Business, Management and Administration. 2012
National Association of State Directors of Career Technical Education Consortium. Washington, DC
Business Education Standards. National Business Education Association. Reston, VA.
Berenson, Levine, Krehbiel. Basic Business Statistics Text, Concepts and Applications. 11th edition. 2011. Pearson Prentice
Hall, Upper Saddle River, NJ.
Applied Statistics – Lesson 8; Hypothesis Testing. Andrews University, Berrien Springs, MI.
Applied Statistics – Lesson 2; Organizing and Presenting Data. Andrews University, Berrien Springs, MI.
Applied Statistics – Lesson 6; Linear Regression. Andrews University, Berrien Springs, MI.
What is Hypothesis Testing?; Data Collection Methods; Survey Sampling Methods; What is Linear Regression?; and What is Probability
Distribution? Stat Trek. http://stattrek.com/
Introduction to Statistics Course Competencies. 2010. Technical College System of Georgia. Atlanta, GA.
Elements of Statistics Course Objective Outline. 2007. Western Maricopa Education Center, Glendale, AZ.
Statistics for Business Course Syllabus. 2011. The University of Iowa, Iowa City, Iowa.
Problems in Statistics – Regression Analysis. Middle Tennessee State University, Murfreesboro, TN.
Donnelly, Robert A. The Complete Idiot’s Guide to Statistics. 2007. Penguin Group, New York, NY.
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