Elementary Statistical Methods

Competencies

1. To demonstrate competency in explaining the use of data collection and statistics as tools to reach reasonable conclusions, the student should be able to:
   1. Use the proper terms to be able to communicate statistical ideas.
   2. Determine the difference between descriptive statistics and inferential statistics.
   3. Demonstrate an ability to understand the statistical terms that are commonly used in textbooks, newspapers, magazines, and on television and radio in society today.
2. To demonstrate competency in understanding and using frequency distributions and graphs to describe data, the student should be able to:
   1. Organize a frequency distribution.
   2. Draw histograms to illustrate data in frequency distributions.
   3. Interpret and draw other commonly used graphs including time series graphs, Pareto charts, pie graphs, and stem and leaf plots.
3. To demonstrate competency in recognizing, examining and interpreting the basic principles of describing and presenting data, the student should be able to:
   1. Calculate and interpret common measures of central tendency such as mean, median, and mode using both grouped and ungrouped data.
   2. Calculate a weighted mean.
   3. Calculate and interpret common measures of variability such as range, standard deviation, and variance for both grouped and ungrouped data.
   4. Calculate z-scores (standard scores) and quartiles to determine the relative positions of raw scores in a data set.
   5. Use the Empirical Rule to describe data that are bell shaped, and use Chebyshev's Inequality to describe any sets of data.
   6. Determine and interpret the interquartile range.
   7. Determine outliers for a set of data.
   8. Draw box plots for data sets.
4. To demonstrate competency in computing and interpreting empirical and theoretical probabilities using the rules of probabilities and combinatorics, the student should be able to:
   1. Calculate probabilities by using sample spaces.
   2. Determine the complement of an event and to calculate the corresponding probability.
   3. Recognize the difference between classical, empirical, and subjective probability.
   4. Calculate probability using the addition rules.
   5. Recognize mutually exclusive events in order to correctly calculate the corresponding probabilities.
   6. Find the probability of two or more independent events.
   7. Find the probability of two or more dependent events.
   8. Apply the formula for conditional probability.
   9. Calculate probabilities using terms such as “and,” “or,” and “at least one.”
   10. Use tree diagrams as a counting technique.
   11. Calculate with counting techniques using multiplication rules.
   12. Recognize permutations and to count outcomes using permutation formulas.
   13. Recognize combinations and to count outcomes using combination formulas.
   14. Use counting rules to find probabilities.
5. To demonstrate competency in examining, analyzing and comparing various sampling distributions for both discrete and continuous random variables, the student should be able to:
   1. Construct a probability distribution for a random variable.
   2. Determine the mean, variance, standard deviation, and the expected value for a discrete random variable.
   3. Compute probabilities of binomial experiments.
   4. Compute the mean and standard deviation of a binomial random variable.
6. To demonstrate competency in analyzing data by comparing to the normal distribution, the student should be able to:
   1. Identify distributions as symmetrical or skewed.
   2. Identify the properties of the normal distribution.
   3. Find the area under the standard normal distribution given various z values.
   4. Find probabilities for a normally distributed variable by transforming it into a standard normal variable.
   5. Find specific data values for given percentages using the standard normal distribution.
   6. Use the central limit theorem to solve problems involving sample means for large and small samples
   7. Use the normal approximation to compute probabilities for a binomial variable.
   8. Compute probabilities of a sample proportion.
7. To demonstrate competency in describing and computing confidence intervals, the student should be able to:
   1. Find the confidence interval for the mean.
   2. Find confidence intervals and sample size for proportions.
8. To demonstrate competency in performing hypothesis testing using statistical methods, the student should be able to:
   1. Understand the definitions used in hypothesis testing.
   2. State the null and alternative hypotheses.
   3. Find critical values.
   4. State the five steps used in hypothesis testing.
   5. Test means using the t test.
   6. Test proportions using the z test.
   7. Explain the relationship between type I and type II errors.
   8. Test the difference between two large sample means using the z test (optional).
   9. Test the difference between two proportions using the z test (optional).
9. To demonstrate competency in solving linear regression and correlation problems, the student should be able to:
   1. Draw a scatter plot for a set of ordered pairs.
   2. Find the Pearson product moment correlation coefficient.
   3. Determine whether a linear relationship exists between two variables.
   4. Find the equation of the regression line.
   5. Make predictions when an appropriate correlation exists.

Campus Resources for Students

Weatherford:
The Academic Support Center is a free public tutoring service provided by the college, offered in LART- LL Room 2, 817-598-6278

Video tapes

Computer assisted instruction

Instructor’s office hours