Advanced Statistics and probability theories

Description

After careful study of this chapter, you should be able to do the following:

1.Explain the general concepts of estimating the parameters of a population or a probability distribution

2.Explain the important role of the normal distribution as a sampling distribution and the central limit theorem

3.Explain important properties of point estimators, including bias, variances, and mean square error

4.Construct point estimators using the method of moments and the method of maximum likelihood.

5.Compute and explain the precision with which a parameter is estimated

6.Construct a point estimator using the Bayesian approach

8- After careful study of this chapter, you should be able to do the following:

1.Construct confidence intervals on the mean of a normal distribution, using normal distribution or t distribution method

2.Construct confidence intervals on the variance and standard deviation of normal distribution

3.Construct confidence intervals on a population proportion

4.Use a general method for constructing an approximate confidence interval on a parameter

5.Construct a prediction interval for a future observation

6.Construct a tolerance interval for a normal population

7.Explain the three types of interval estimates: confidence intervals, prediction intervals, and tolerance intervals

9- After careful study of this chapter, you should be able to do the following:

1.Structure engineering decision-making problems as hypothesis tests

2.Test hypotheses on the mean of a normal distribution using a Z-test or a t-test

3.Test hypotheses on the variance or standard deviation of a normal distribution

4.Test hypotheses on a population proportion

5.Use the P-value approach for making decisions in hypothesis tests

6.Compute power & Type II error probability and make sample size selection decisions for tests on means, variances and proportions

7.Explain & use the relationship between confidence intervals & hypothesis tests

8.Use the chi-square goodness-of-fit test to check distributional assumptions

9.Apply contingency table tests

10.Apply nonparametric tests

11.Use equivalence testing

12.Combine P-values

10- After careful study of this chapter, you should be able to do the following:

1.Structure comparative experiments involving two samples as hypothesis tests

2.Test hypotheses and construct confidence intervals on the difference in means of two normal distributions

3.Test hypotheses and construct confidence intervals on the ratio of the variances or standard deviations of two normal distributions

4.Test hypotheses and construct confidence intervals on the difference in two population proportions

5.Use the P-value approach for making decisions in hypothesis tests

6.Compute power, Type II error probability, and make sample size decisions for two-sample tests on means, variances & proportions

7.Explain and use the relationship between confidence intervals and hypothesis tests

11- After careful study of this chapter, you should be able to do the following:

1.Use simple linear regression for building empirical models to engineering and scientific data

2.Understand how the method of least squares is used to estimate the parameters in a linear regression model

3.Analyze residuals to determine if the regression model is an adequate fit to the data or to see if any underlying assumptions are violated

4.Test the statistical hypotheses and construct confidence intervals on the regression model parameters

5.Use the regression model to make a prediction of a future observation and construct an appropriate prediction interval on the future observation

6.Apply the correlation model

7.Use simple transformations to achieve a linear regression model

TAKE THIS COURSE