MATH141

To introduce students to the fundamental concepts of probability.

To present the basic techniques used in descriptive and inferential statistics.

To introduce students to the use of technology for data exploration and analysis.

To encourage students to communicate effectively in presenting the results of a statistical study. This may include (but not be limited to) emphasis on reading, problem solving, and writing skills throughout the course as they are needed in the practice of statistics.

Data Types

1. Distinguish between a population and a sample, between a parameter and a statistic, and between descriptive and inferential statistics.

2. Distinguish between qualitative data and quantitative data.

3. Classify data with respect to the four levels of measurement.

4. Identify the different types of sampling techniques.

Descriptive Statistics

1. Construct frequency distributions, frequency histograms, frequency polygons, relative frequency histograms, stem-and-leaf, and box-and-whisker plots.

2. Find and interpret the mean, median, and mode of a population and of a sample.

3. Find and interpret the range, variance, and standard deviation of a population and of a sample.

4. Interpret standard deviation by means of the Empirical Rule and Chebychev’s theorem.

5. Find and interpret quartiles, percentiles and interquartile range of data set.

6. Find and interpret the standard score (z-score).

Probability

1. Identify the sample space of a probability experiment and identify simple events.

2. Distinguish between classical, empirical, and subjective types of probability.

3. Distinguish between dependent and independent events.

4. Determine if two events are mutually exclusive.

5. Calculate probabilities through the use of the Complement Rule, the Multiplication Rule, and the Addition Rule.

Discrete Probability Distributions

1. Distinguish between discrete random variables and continuous random variables.

2. Construct a discrete probability distribution and its graph.

3. Determine if a function is a probability distribution, and find the mean, standard deviation, and expected value of the distribution.

4. Find binomial probabilities using the binomial probability formula.

5. Find the mean and standard deviation of a binomial probability distribution.

Normal Probability Distributions

1. Find probabilities for normal distributions using both tables and technology.

2. Find specific data values of a normal distribution associated with a given probability using both tables and technology.

3. Verify the properties of sampling distributions.

4. Apply the Central Limit Theorem to find the probabilities associated with sample means.

Confidence Intervals

1. Construct and interpret confidence intervals for a population mean using both small and large sample techniques by means of tables and technology.

2. Construct and interpret confidence intervals for a population proportion by means of tables and technology.

3. Construct and interpret confidence intervals for the difference of proportions or means for two populations.

4. Determine the minimum sample size required when estimating the population mean and population proportion.

5. Construct and interpret confidence intervals for the population variance and standard deviation by means of both tables and technology.

Hypothesis Testing Using a Simple Sample

1. Conduct and present formal hypothesis tests involving the mean of a population using both small and large sample techniques.

2. Conduct and present formal hypothesis tests involving a population proportion.

3. Conduct and present formal hypothesis tests involving the standard deviation (or variance) of a population using a sample drawn from a normal population.

Hypothesis Testing with Two Samples

1. Conduct and present a hypothesis test for the difference between two population means using techniques for large independent samples, small independent samples, and dependent samples.

2. Conduct and present a hypothesis test for the difference between two population proportions.

Correlation and Regression

1. Determine the coefficient of correlation for a sample of bivariate data by means of technology and interpret the value in the context of the data.

2. Conduct and present a hypothesis test for the significance of a population correlation coefficient.

3. Determine the equation of a regression line for bivariate data by means of technology and use the equation to make predictions.

4. Determine the coefficient of determination for a sample of bivariate data by means of technology and interpret the value in the context of the data.

Chi-Square Tests and the F-Distribution

1. Test whether a frequency distribution fits a claimed distribution through use of the chi-square distribution.

2. Test whether two variables are independent by means of contingency tables and the chi-square distribution.

3. Perform a two-sample F-test to compare two variances.

4. Test claims involving three or more means through use of one-way-analysis of variance (ANOVA).

Nonparametric Tests

1. Test a population median and the difference between two population medians through use of the nonparametric Sign Test.

2. Determine if two samples (both independent and dependent) are selected from populations with the same distribution through use of the nonparametric Wilcoxon Tests.

3. Determine if three or more samples were selected from populations with the same distribution through use of the Kruskal-Wallis Test.