Lecture_9_Slides_486609574.pdf

# Lecture_9_Slides_486609574.pdf - I NTRODUCTORY E...

• Notes
• 56

This preview shows pages 1–10. Sign up to view the full content.

I NTRODUCTORY E CONOMETRICS Lecture 9 Spring 2017, Tsinghua University Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 1 / 60

This preview has intentionally blurred sections. Sign up to view the full version.

Hypothesis Test and Confidence Intervals Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 2 / 60
O UTLINE 1 Rejection Region Method 2 p-value Approach 3 Choose between "Valid" Decision Rules 4 Confidence Interval Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 3 / 60

This preview has intentionally blurred sections. Sign up to view the full version.

H YPOTHESIS T EST : G ENERAL S TEPS We begin with a null H 0 and alternative hypothesis H 1 . The testing procedure begins with the assumption that H 0 is true. The goal is to determine whether there is enough evidence in the data to support H 1 . There are only two possible decisions: 1 Conclude that there is enough evidence to support H 1 . 2 Conclude that there is not enough evidence to support H 1 . The decision rule revolves around = Pr ( Type I error ) = Pr ( H 0 being rejected | H 0 is true ) Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 4 / 60
T ESTING M ETHODS There are two general approaches: 1 The rejection region method. 2 The p-value approach. We will describe how each of these approaches works in both two-tail and one-tail hypothesis tests. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 5 / 60

This preview has intentionally blurred sections. Sign up to view the full version.

In this course, we are primarily interested at testing about the regression coefficient β j ’s. Yet, we will start with tests about the population mean μ . Note: we will, at first, maintain the assumption that the population standard deviation σ is known. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 6 / 60
R EJECTION R EGION M ETHOD All tests about the population mean μ are based on looking at the sample average X . The rejection region method works by establishing a region of values such that we reject H 0 whenever X Falls inside this region. The features of the rejection region depend on: 1 The significance level we want to achieve. 2 Whether we have a one-tail or a two-tail test. Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 8 / 60

This preview has intentionally blurred sections. Sign up to view the full version.

R EJECTION R EGION M ETHOD WITH O NE - TAIL T ESTS First, we begin with a pre-specified significance level (we get to choose this). Recall that is defined as: Pr ( Rejecting H 0 when it is true ) . Now, suppose our test is H 0 : μ = μ vs H 1 : μ > μ . Intuitively: Since X is a consistent estimator of μ , we would have evidence in favor of H 1 if X - μ is “large”. According to this logic, we should reject H 0 in favor of H 1 if X - μ > x L Where x L is a cut-off value. How do we determine x L by making sure that we achieve the significance level that we pre-specified? For this, we invoke the Central Limit Theorem . Shengjie Hong (SEM, Tsinghua) [email protected] Lecture 9 9 / 60
That is, we choose x L in order to satisfy Pr ( Rejecting H 0 when it is true ) = .

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Spring '16
• Hong Shengjie

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern