MTH 160 STATISTICS I

The purpose of this course is to introduce the student to Statistics in a way that will make the student aware of the techniques of Statistics as they apply to the solutions of practical problems in various fields. This introduction will be presented with particular attention to statistical vocabulary, problem solving, and point of view. The individual instructor is required to prepare and administer a comprehensive final exam testing the degree of mastery of the following course objectives:

1. Descriptive Statistics

1.1 Define the terms population, sample (large and small), statistical experiment, variable (discrete and continuous), data (attribute and variable), statistic, and parameter.

1.2 Define and use simple random sampling techniques.

1.3 Explain why the mean, median and mode are examples of statistics which are measures of central tendency, and compute these measures using appropriate formulas and technology.

1.4 Explain why the range, variance, and standard deviation are examples of statistics which are measures of variation (or dispersion) and compute these measures using appropriate formulas and technology.

1.5 Explain why the standard score (z-score), quartiles, and percentiles are measures of position and compute these measures.

1.6 Describe the relationship between a sample statistic and its corresponding population parameter.

1.7 Explain what grouped and ungrouped frequency distributions are. Construct them for large samples.

1.8 Graphically display a histogram and a box-and-whiskers display. Other graphs such as a stem-and-leaf display, ogive, bar graph, dotplot, circle graph (pie chart) and Pareto diagram are optional.

1.9 Describe the characteristics of the distributions: normal, uniform or rectangular, skewed, and bimodal.

1.10 Explain that there are three major features of interest when describing the distribution of a sample or population:

a  its shape (pattern of variability)
b  its central tendency
c  its dispersion.

2. Correlation and Regression

2.1 Define the terms bivariate data, data point, scatter diagram, regression line, method of least squares, regression coefficients, correlation coefficient.

2.2 Construct a scatter diagram and find (using appropriate formulas or technology) the equation of the least squares regression line, and sketch the regression line through the data points.

2.3 Explain what correlation is, why correlation analysis is performed, and find (using appropriate formulas or technology) and interpret r.

2.4 Explain what linear regression is, why regression analysis is performed, and interpret the least squares regression line.

3. Probability

3.1 Define the terms probability, simple probability experiment, sample space, event, simple event, compound event, complement, mutually exclusive, dependent events, independent events, and conditional probability.

3.2 Calculate the probabilities of simple and compound events using relative frequency.

3.3 Apply the addition and complement rules of probability when appropriate.

4. Discrete Probability Distributions

4.1 Describe what a random variable is (both discrete and continuous).

4.2 Explain what a discrete probability distribution is and how to construct one.

4.3 Graphically display, without technology, a discrete probability distribution by means of a histogram.

4.4 Calculate probabilities from a discrete probability distribution.

4.5 Calculate the mean of a discrete random variable.

5. Binomial Probability Distribution

5.1 Describe the characteristics of a binomial probability experiment.

5.2 Determine whether a variable is or is not a binomial variable.

5.3 Explain why a binomial variable is an example of a discrete random variable.

5.4 Explain that the parameters of the binomial distribution are n and p and that the possible values of the binomial random variable are the integers from zero to n, inclusive.

5.5 Calculate probabilities of the binomial random variable using at least one of the following: binomial formula, binomial probability table, Minitab.

5.6 Use the addition rule and complement rule to find probability for multiple values of the binomial random variable.

5.7 Compute µ and s for a binomial distribution using the appropriate distribution formulas.

6. Normal Probability Distribution

6.1 Explain why the normal variable is an example of a continuous random variable.

6.2 Explain why µ and s are the parameters of this distribution and describe the following characteristics of the normal distribution:

a  the mean equals the median.
b  symmetry about the mean.
c  total area beneath curve is 1.
d  substantiates Empirical Rule.

6.3 Calculate probabilities associated with a normal variable and the values of a normal variable given an associated probability using at least one of the following methods:

a  normal tables
b  statistical calculator
c  Minitab

6.4 Demonstrate that area, proportion of population, and probability are equivalent notions for continuous probability distributions.

7. Sampling Distribution

7.1 Describe what a sampling distribution is and the method to approximate one for any sample statistic.

7.2 State and apply the Central Limit Theorem.

8. Statistical Inference - Estimation and Hypothesis Testing

8.1 Explain and define the parts of the estimation process: point estimate, level of confidence, maximum error of estimate, and confidence interval.

8.2 Explain and define the parts of the hypothesis testing process: null hypothesis, alternative hypothesis, level of significance (as related to Type I and Type II errors), test statistic, p-value, decision and conclusion.

8.3 Describe what the Student's t-distribution is, and how it compares with the normal distribution.

8.4 Construct confidence intervals for µ and p using the appropriate statistics for any level of confidence and explain the meaning of the interval in the context of the problem.

8.5 Describe the general procedure for any hypothesis test. Complete the following hypothesis tests and explain the conclusion in the context of the problem:

a  test µ (using both z and t as test statistics).
b  test p (using z as the test statistic).

9. Statistical Project

Demonstrate in at least one project the understanding that statistics is the study of how to collect, organize, analyze, interpret, and present numerical information. Project components may be done by hand and/or using Minitab. An example of a project:

• Collect at least 30 pieces of data.
• Organize the data.
• Determine such statistics as the mean, median, mode, range, percentiles, and quartiles.
• Group the data into a frequency distribution.
• Illustrate the data graphically using at least one of the following: histogram, dotplot, stem-and-leaf, etc.
• Interpret data with respect to Empirical Rule or Chebyshev’s Theorem.
• Present all of the above in a neat and accurate form.

10. Statistical Computer Software (Minitab)
*Use the appropriate Minitab commands to produce and print the following:

10.1 At least one graph-type for univariate data. (for example: histogram, dotplot, stem-and-leaf, box-and-whisker plot, etc.)

10.2 Descriptive univariate statistics including: mean, median, range and standard deviation.

10.3 A scatter diagram of bivariate data.

10.4 The correlation coefficient (r) and the linear regression equation for bivariate data.

10.5 A confidence interval for the mean.

10.6 A hypothesis test for the mean.

* The instructor is encouraged to use additional Minitab commands.

(revised 06/08/05)