# Statistical Analysis

Category: Objective TestType: Individual

### Overview

60-minute test administered during the NLC.

**Objective Test Competencies**:
Descriptive Statistical Analysis; Organizing and Presenting Statistical Data; Probability Distributions; Sampling Techniques; Linear Regression; Confidence Integrity; Hypothesis Testing

**Skills**: This event provides recognition for PBL members who demonstrate knowledge of, and the ability to, apply common techniques and statistical analysis tools.

### Guidelines

#### Objective Test Guidelines

- No materials may be brought to the testing site.
- Electronic devices must be turned off and out of sight.
- Financial calculators may be used for accounting, finance, and analysis & decision making events; calculators will be provided for all other events.

The general event guidelines below are applicable to all national competitive events. Please review and follow these guidelines when competing at the national level. When competing at the state level, check the state guidelines since they may differ.

#### Eligibility

- Dues: Competitors must have paid PBL national and state dues by 11:59 p.m. Eastern Time on April 15 of the current school year.
- NLC Registration: Participants must be registered for the NLC and pay the national conference registration fee in order to participate in competitive events.
- Deadlines: The state chair, or designee, must register each state competitor on the official online entry forms by 11:59 p.m. Eastern Time on the second Friday in May.
- Each state may submit three (3) individuals in all events requiring only objective tests and two (2) individuals or teams for all events that require a pre-judged or performance component.
- Each competitor can compete in two (2) events.
- Each competitor must compete in all parts of an event for award eligibility.
- A team shall consist of two or three members. Exceptions are Parliamentary Procedure which must be a team of four or five members, and LifeSmarts which must be a team of two members.

#### Repeat Competitors

Competitors are **not** permitted to compete in an event more than once at the national level unless one of the following circumstances applies:

- Modified Events: A competitor may compete in the same event when the event is modified. Note, if the only modification is a name change, competitors may
**not**compete in the renamed event. - Team Events: One (1) competitor of the team may have competed in the same event at one (1) previous NLC; however, they may not compete more than twice in the event at the national level.
- Chapter Events: Competitors may compete in a chapter event more than once (Community Service Project).
- Individual Entry: A competitor who competed as an individual entry in a team event at the national level may compete in the same event a second time as part of a team, but not a second time as an individual.
- Parliamentary Procedure: Two (2) competitors of the team may have competed in this event at a previous NLC; however, they may not compete more than twice at the national level.
- Pilot Event: Competition in a pilot event does not disqualify a competitor from competing in the same event if it becomes an official competitive event. The participant may compete in another event as well as a pilot event.

#### Breaking Ties

- Objective Tests: Ties are broken by comparing the correct number of answers to the last 10 questions on the exam. If a tie remains, the competitor who completed the test in a shorter amount of time will place higher. If this does not break the tie, answers to the last 20 questions will be reviewed and determine the winner.
- Objective and Production Tests: The production test scores will be used to break a tie.
- Objective Tests and Performances: The objective test score will be used to break a tie based on the tie-breaking criteria of objective tests.
- Reports/Projects and Performances: The report/project scores will be used to break a tie.
- Performances: Judges must break ties and all judges’ decisions are final.

#### National Deadlines

- State chair/adviser must register all competitors for NLC competitive events online by 11:59 p.m. Eastern Time on the second Friday in May.
- All prejudged components (report PDFs, resume/letter of application PDFs, and project URLs) must be received by 11:59 p.m. Eastern Time on the second Friday in May.
- All URLs and PDFs for prejudged projects and reports will be submitted by the state adviser via the competitive events registration form.
- All production tests must be received at FBLA-PBL by 11:59 p.m. Eastern Time on the third Friday in May.
- Desktop Publishing—the finished product must be uploaded in PDF format by 11:59 p.m. Eastern Time on the third Friday in May. Label all documents with the event title, competitor’s name, state, and school.
- All production tests must be uploaded online.
- State chair/adviser may make name changes only (no additional entries) by 11:59 p.m. Eastern Time on the first Friday in June. Competitor drops are the only changes allowed after this date and onsite.

#### National Awards

The number of competitors will determine the number of winners. The maximum number of winners for each competitive event is 10. Only one (1) award is given to the schools competing in chapter events (Community Service Project and Local Chapter Annual Business Report).

#### Additional Materials

- Financial calculators may be brought to objective testing and used for any accounting, finance, or analysis & decision making events.
- Certain events may allow the use of additional materials. Please refer to event guidelines.

#### Americans with Disabilities Act (ADA)

FBLA‑PBL meets the criteria specified in the Americans with Disabilities Act for all participants who submit a special needs form.

#### Recording of Presentations

No unauthorized audio or video recording devices will be allowed in any competitive event. Participants in the performance events should be aware the national association reserves the right to record any performance for use in study or training materials.

#### Graduate Students

Graduate students may compete in all PBL events.

### Preparation

##### Sample Practice Materials

##### Format Guide

##### Website Resources

- Statistical Analysis of Multiple Choice Exams
- Understanding Research Results: Statistical Inference
- Probability Distribution: List of Statistical Distributions
- Sampling method

**Descriptive Statistical Analysis**

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.

**Organizing and Presenting Statistical Data**

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.

**Probability Distributions**

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.

**Sampling Techniques**

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.

**Linear Regression**

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

**Confidence Integrity**

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.

**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 assump

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).