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# Probability and Probability Distributions

Title: Probability and Probability Distributions

Course Code: STAT-102

Credit Hours: 03

Prerequisite: Elementary Statistics

## Course Objectives:

This course is designed to equip students with higher statistical tools and their application in economic analysis.

## Course Contents:

Random Variables and Discrete Probability Distribution Random variables, discrete random variable, continuous random variable, discrete probability distribution; The mean, variance and standard deviation of a probability distribution; binomial probability distribution, and its computation. Cumulative probability distributions, properties of binomial probability distribution.

## Continuous Probability Distribution

Continuous probability distribution: the normal probability distribution: properties of normal distribution, Applications of the standard normal distribution, finding areas under the normal curve.

## Sampling and Sampling Distributions

What is sampling? Defining population, determining sampling frame, sampling design (probability versus non-probability sampling) and appropriate sample size. Issues of precision and confidence in determining a sample size. Sampling with and without replacement, sampling and non-sampling error, sampling bias; sampling distribution of the mean; The central limit theorem; sampling distribution of differences between means; sampling distribution of sample proportion; sampling distribution of differences between proportions.

## Estimation and Confidence Intervals

Point estimates and confidence intervals; estimation by confidence interval: confidence interval estimate of a population mean (known variance), confidence interval estimate of a population mean (unknown variance) confidence interval for differences of means, confidence interval for differences of means; confidence interval for population proportion, confidence interval for differences between proportions.

## Hypothesis Testing

One sample test of hypothesis; one sample; one tail and two tails tests of significance; testing for a population mean with a known population standard deviation: two-tailed test, one- tailed test; P-value in hypothesis testing; testing for a population mean: large sample, population standard deviation unknown.

## Chi-Square Applications

Introduction; goodness-of-fit test: equal expected frequencies; goodness-of-fit test: Unequal expected frequencies; limitations of Chi-square.

## Analysis of Variance

Introduction, the F-distribution; comparing two population variances; ANOVA assumptions; ANOVA test; inferences about pairs of treatment means; two-way analysis of variance.

## Recommended Books:

• Anderson, D. R., Sweeney, D. J., Williams, T. A., Camm, J. D., & Cochran, J. J. (2014). Essentials of statistics for business and economics. Cengage Learning.
• Anderson, D. R., Williams, T. A., & Sweeney, D. J. (2011). Statistics for Business and Economics. 12th. Cengage Learning.
• Lind, Douglas A., Marshal, William G. and Mason, Robert D., (2015) Statistical Techniques in Business and Economics (16th edition). Boston: McGraw Hill, 2003.