×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

by: Shane Marks

9

0

6

# INTRO STAT THEORY II STAT 703

Shane Marks

GPA 3.93

Staff

These notes were just uploaded, and will be ready to view shortly.

Either way, we'll remind you when they're ready :)

Get a free preview of these Notes, just enter your email below.

×
Unlock Preview

COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
6
WORDS
KARMA
25 ?

## Popular in Statistics

This 6 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 703 at University of South Carolina - Columbia taught by Staff in Fall. Since its upload, it has received 9 views. For similar materials see /class/229670/stat-703-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.

×

## Reviews for INTRO STAT THEORY II

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 10/26/15
STAT 703J703 February 8th 2005 Lecture 9 lnstructor Brian Habing Department of Statistics LeConte 203 Telephone 8037773578 Email habingstatscedu STAT 7amp31703 BHabing Univ of SC Today Homework 3 Solutions Basics of Hypothesis Testing Chapter 9 STAT 7amp31703 BHabing Univ of SC w Ch85 Suppose that X follows a geometric distribution PX k Iva p And assume an iid sample of size n b Find the mle of 0 STAT 7amp31703 BHabing Univ of SC w c Find the asymptotic variance of the MLE v STAT 7amp31703 BHabing Univ of SC M Ch86 Consider the data Hops Freg Hops Freg 1 48 7 4 2 31 8 2 3 20 9 1 4 9 10 1 5 6 11 2 6 5 12 1 a Fit a geometric distribution b Find an approximate 95 confidence interval for p v STAT 7amp31703 BHabing Univ of SC M Ch844c Let X1Xn be iid random variables with density function fx661x 90 x 1 Find the asymptotic variance of the MLE v STAT 7amp31703 BHabing Univ of SC M Statistical Inference Confidence Intervals and Tests of Hypotheses Test of hypothesis general method to distinguish between 2 or more probability distributions or models based on a sample X1 Xn assumed to come from one of them v STAT 7amp31703 BHabing Univ of SC 4 M In particular based on X1 Xn decide whether f1x or f2x is the pdf or population from which the sample came More specifically suppose we think the sample is from a normal population with mean either u5 or u10 with variance 4 Or more generally uu1 vs uu2 STAT 7amp31703 BHabing Univ of SC M To do this we follow the Neyman Pearson Paradigm and discuss significance tests NeymanPearson Approach Group the possible hypothesized distributions into two categories the null hypothesis HO and the alternative h othesis HA research hypothesis V STAT703J703 BHabing Univ ofSC 10 Lg Observe X1 Xn Either H0 Np1 62 or HA Np2 62 or H0 pp1 vs HA pp2 p is the mean of Np 62 Here if 02 is known each of these hypotheses completer specifies the distribution or population 80 HO and HA are called simple hypotheses v STAT 7amp31703 BHabing Univ of SC 4 w n If H0 u0 VS HA u gt 0 u in Nu 62 with 02 known Then H0 is simple and HA is a composite hypothesis ie several normal distributions would satisfy it HA is also referred to as a onesided hypothesis v STAT 7amp31703 BHabing Univ of SC 12 M If H0 u0 VS HA who u in Nu 62 02 known then HA is a twosided composite hypothesis Next we set up the framework for testing HO and HA based on the sample v STAT 7amp31703 BHabing Univ of SC 13 M 92 NevmanPearson Paradigm Let x X1 Xn denote a sample from population fxe Decide on HO vs HA based on the sample A decision on whether or not to reject H0 in favor of HA is made on the basis of a statistic TTXTX1 Xn w STAT 7amp31703 BHabing Univ of SC 14 M The set of values of T for which H0 is accepted is called the acceptance region and the set of values of T for which H0 is rejected is the reiection region of the test v STAT 7amp31703 BHabing Univ of SC 15 M Two kinds of error may occur 1 H0 is rejected when it is true Type I error Ptype I error or PT e rejection region HO true If H0 is simple or is called the significance level of the test v STAT 7amp31703 BHabing Univ of SC 16 M 2 H0 is accepted when it is false Type II error Ptype ll error 3 PT in acceptance region HO false If HA is composite 3 depends on which member of HA is the true pdf v STAT 703J703 BHabing Univ of SC 4 w 17 Power of the test PHO is rejected when false 1 PHO is accepted HO false 1 3 Ideally we would want oc30 but this not possible since the decision is based on data v STAT 703J703 BHabing Univ of SC 18 M

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Allison Fischer University of Alabama

#### "I signed up to be an Elite Notetaker with 2 of my sorority sisters this semester. We just posted our notes weekly and were each making over \$600 per month. I LOVE StudySoup!"

Bentley McCaw University of Florida

#### "I was shooting for a perfect 4.0 GPA this semester. Having StudySoup as a study aid was critical to helping me achieve my goal...and I nailed it!"

Parker Thompson 500 Startups

#### "It's a great way for students to improve their educational experience and it seemed like a product that everybody wants, so all the people participating are winning."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com