Probability and Statistic Final Report

[pic 1]INTERNATIONAL UNIVERSITY
Lecturer: Hồ Thanh Vũ

PROBABILITY AND STATISTICS COURSE
FINAL PROJECT

Group:Trần Thị Ngọc Quỳnh-IELSIU15105
                Thái Nguyên Phú-IELSIU15095
                Huỳnh Dương Mỹ Hương-
                Bùi Khánh Vân-
                Lê Nguyễn Trọng Hiển-
                Phan Minh Quân-

OUTLINE:

• Literature Review
• Methodology & Task Allocation
• Actual work on questions
• Conclusion
• Reference

LITERATURE REVIEW:

        In this project, there are two big questions, including 9 more small questions about three big chapters in the Probability and Statistics course, which are Hypothesis testing, Anova and Regression.
HYPOTHESIS TESTING:
What is a hypothesis?
        A hypothesis is a specific, testable prediction. It describes in concrete terms what you expect will happen in a certain circumstance, it is called “hypothesis” because it is not justified. Hypothesises are used to determine the whether a statement is true or false, each hypothesis implies its alternative hypothesis covering all the situations which are not in the null hypothesis. The hypothesis used to test is called null hypothesis, and the contrary ones called alternative hypothesis. The null hypothesis is true until it is rejected. The null and alternative hypothesis exist independently and only one of them can be true.
Example: Null hypothesis(Ho): M=0
           Alternative hypothesis(H1): M#0
How to do the hypothesis testing?
        The method to do the hypothesis testing is getting a sample from a population and calculate its descriptive statistics, basing on the test statistics and significant level, the conclusion is whether to reject the null hypothesis or not. There are many types of hypothesis for each kind of sample and the claim.
        The test statistics is the sample statistics computed from the data collected, the value of the test statistics will determine whether to reject Ho or not.
        The rejection region of a statistical hypothesis test is the range of numbers that will lead us to reject the null hypothesis in case the test statistic falls within this range.  The rejection region is defined by the critical points, which is defined by the significant level α given and the sample’s distribution.
        The non-rejection region, is the range of numbers that will lead us not to reject the null hypothesis in case the test statistics fall wtithin this range, the probability falling is 1- α.
There are two types of errors which could happen in the test. The first is to reject the null hypothesis while it is true, called type I error (α). The second is to accept the null hypothesis while it is indeed wrong, called type II error (β). In science and reality, the type I error is not as dangerous as type II error. The probability of type I error is denoted by α-also called level of significance of the test. The probability of type II error is denoted by β, 1-β is the power of the test.
        P-value, is defined as the probability of obtaining a value of the test statistic as extreme as, or more extreme than, the actual value obtained, when the null hypothesis is true.
Two-tailed and one-tailed test:
        When the alternative hypothesis test is H1: M#0, then it is a two-tailed test, the rejection region is located two tails of the distribution.
        When the alternative hypothesis test is H1: M>0, then it is a one-tailed test, the rejection region is located on the right tail of the distribution, so we call it right-tailed test.
And base on the common logic, when the hypothesis test is: H1: M<0, then it is a one-tailed test, and the rejection region therefore is on the left, so it is left-tailed test.