# MAT 282 STATISTICS 3 cr. (3-0) (online sections)

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1 JOHN A. LOGAN COLLEGE J. Dethrow SM 11 MAT 282 STATISTICS 3 cr. (3-0) (online sections) COURSE DESCRIPTION: MAT 282 is designed to meet the needs of students requiring a statistics course with a college algebra prerequisite in their programs. Topics include descriptive statistics, including graphical and numerical, basic probability theory, probability distributions, inferences involving estimation, and hypothesis testing, correlation and regression, and analysis of variance. The Texas Instruments TI-83 or TI-84 graphing calculator or a calculator approved by the instructor is required for this course. MAT 282 is ordinarily offered in the summer semester only. PREREQUISITES: MAT 108 with a grade of C or higher or assessment UCOURSE OBJECTIVES: 1. Compute the mean, median, mode, and standard deviation of a data set. 2. Compute the expected value and standard deviation of a distribution. 3. Construct a histogram from a data set or probability distribution. 4. Construct a box-plot and interpret the five-number summary. 5. Apply counting principles for computing probabilities. 6. Compute probabilities for a discrete random variable to assume a distinct value or a range of values when the distribution is general, binomial, or Poisson. 7. Compute probabilities for a continuous random variable to assume a range of values when the distribution is normal via the normal table and via TI-83 calculator. 8. Compute the z-value for a continuous random variable. 9. Apply the Central Limit Theorem to the sampling distribution of means. 10. Calculate a confidence interval for a population mean using large samples. 11. Calculate a confidence interval for a population mean using small samples. 12. Calculate a confidence interval for a population proportion using large samples. 13. Calculate a confidence interval for a difference of population means using large samples. 14. Calculate a confidence interval for a difference of population means using small samples. 15. Calculate a confidence interval for a difference of population proportions using large samples. 16. Compute an appropriate sample size satisfying criteria for a large sample. 17. Apply procedures to establish and properly conclude a hypothesis test for a population mean using large samples.

2 2 18. Apply procedures to establish and properly conclude a hypothesis test for a population mean using small samples. 19. Apply procedures to establish and properly conclude a hypothesis test for a population proportion using large samples. 20. Apply procedures to establish and properly conclude a hypothesis test for a difference of population means using dependent samples. 21. Apply procedures to establish and properly conclude a hypothesis test for a difference of population means using independent samples. 22. Apply procedures to establish and properly conclude a hypothesis test for a difference of population proportions using independent samples. 23. Utilize the P-value in the decision making process of hypothesis testing. 24. Utilize the critical region in the decision making process of hypothesis testing. 25. Determine an equation of the least-squares line in a linear regression analysis. 26. Determine a prediction for an unknown y value in a linear regression analysis. 27. Determine a confidence interval for an unknown y-value in a linear regression analysis. 28. Apply procedures to establish and properly conclude a hypothesis test for the linear correlation between two data sets. COURSE OUTLINE: I. Introduction to Statistics 1.1 Review and Preview 1.2 Statistical Thinking 1.3 Types of Data 1.4 Critical Thinking 1.5 Collecting Sample Data II. III. IV. Summarizing and Graphing Data 2.1 Review and Preview 2.2 Frequency and Distributions 2.3 Histograms 2.4 Statistical Graphics Statistics for Describing, Exploring, and Comparing Data 3.1 Review and Preview 3.2 Measures of Center 3.3 Measures of Variation 3.4 Measures of Relative Standing and Boxplots Probability 4.1 Review and Preview 4.2 Basic Concepts of Probability 4.3 Addition Rule 4.4 Multiplication Rule: Basics 4.7 Counting

3 3 V. Discrete Probability Distributions 5.1 Review and Preview 5.2 Random Variables 5.3 Binomial Probability Distributions 5.4 Mean, Variance, and Standard Deviation for the Binomial Distribution VI. VII. VIII. IX. Normal Probability Distributions 6.1 Review and Preview 6.2 The Standard Normal Distribution 6.3 Applications of Normal Distributions 6.5 The Central Limit Theorem Estimates and Sample Sizes 7.1 Review and Preview 7.2 Estimating a Population Proportion 7.3 Estimating a Population Mean: σ Known 7.4 Estimating a Population Mean: σ Not Known Hypothesis Testing 8.1 Review and Preview 8.2 Basics of Hypothesis Testing 8.3 Testing a Claim About a Proportion 8.4 Testing a Claim About a Mean: σ Known 8.5 Testing a Claim About a Mean: σ Not Known 8.6 Testing a Claim About Variation Inferences from Two Samples 9.1 Review and Preview 9.2 Inferences About Two Proportions 9.3 Inferences About Two Means: Independent Samples 9.4 Inferences from Dependent Samples 9.5 Comparing Variation in Two Samples X. Correlation and Regression 10.1 Review and Preview 10.2 Correlation 10.3 Regression XI. Analysis of Variance 12.1 Review and Preview 12.2 One-Way ANOVA

8 8 John A. Logan College Telephone Numbers Carterville and Williamson County... (618) , (618) Carbondale and Jackson County... (618) , (618) Du Quoin... (618) West Frankfort... (618) Crab Orchard, Gorham, and Trico Areas TTY (hearing-impaired access)... (618) John A. Logan College does not discriminate on the basis of race, religion, color, national origin, disability, age, sexual orientation, or gender orientation a SM 11 rev gh

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