Lecture 1- Inferences concerning two populations_1

Lecture 1- Inferences concerning two populations_1 - 1...

This preview shows pages 1–3. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ECON1320 Quantitative Economic and Business Analysis B LECTURE 1 Introduction to ECON1320 Inferences for Two Populations Ref: Sections 10.4 and 10.5 2 Introduction & Overview r Teaching team: c Lecturers: Vincent Hoang at R441, BLD39A c Tutors r Lectures: two lectures per week on Tuesday and Thursday r Tutorials: two tutorials per week r Consultation: check the timetable on BB 3 Introduction & overview r Assessments c Mid-term exam r Weight: 30% r Topics: the first four lectures r Time: 1 hour plus 10 minutes perusal r Date: 8 Jan 2009 r Location: in this room r Questions format: MCQ & Short answer questions 4 Introduction & overview r Assessments c Final exam r Weight: 70% r Topics: the last seven lectures r Time: 2 hours plus perusal time r Date: Central exam period r Questions format: MCQ & Short answer questions 5 Topics 1. Test the difference between two population proportions using the z statistic 2. Develop a confidence interval estimate for the difference between two population proportions 3. Test for equality of two population variances using the F statistic 6 Proportions r Example: the proportion of female customers or the proportion of defective products r A sample proportion: c x = no. of outcomes (female customers) in a binomial experiment c n=sample size (total number of customers) r Distribution of is (approx) normal if the binomial population is symmetrical [i.e. when both np and n(1-p) >5] x p = n p 2 7 Recall hypothesis tests (in Econ1310) r one tail or two tail test r critical value or p-value approach r 5 steps c state H and H 1 c state decision rule c calculate test statistic (t cal or p-value ) c compare and make a decision c write a conclusion r Use z or t test? c For (use z or t ) c For p , (use z ) c For 1- 2 , (use t ) 8 Now objectives are to 1. Test the difference between two population proportions r Examples: c Question: comparing the proportion of female customers in QLD and Victoria c So we test whether two population proportions obtained from independent samples are equal or not. c Sample 1 (n 1 , ) & sample 2 (n 2 , ) 1 p 2 p 9 One tail or Two tail test & Hypotheses: Lower-tail test: H : p 1 p 2 H 1 : p 1 < p 2 i.e., H : p 1 p 2 H 1 : p 1 p 2 < 0 Upper-tail test: H : p 1 p 2 H 1 : p 1 > p 2 i.e., H : p 1 p 2 H 1 : p 1 p 2 > 0 Two-tail test: H : p 1 = p 2 H 1 : p 1 p 2 i.e., H : p 1 p 2 = 0 H 1 : p 1 p 2 Note: H always contains an equality 10 Two tail test- Step 1: hypotheses H : p 1 = p 2 or H : p 1- p 2 = 0 H 1 : p 1 p 2 or H : p 1- p 2 r H states that the two population proportions are equal . r So the two sample proportions estimate the same value hence can be pooled to obtain an overall estimate of the common p 11 Step 2: the decision rule r Level of significance (e.g. 1%) r Reject H o if critical cal z z 2.575 c z = 2.575 c z = - Non Rejection Region Critical Values Rejection Region 005 ....
View Full Document

This note was uploaded on 10/21/2009 for the course ECON 1320 taught by Professor John during the Three '08 term at Queensland.

Page1 / 10

Lecture 1- Inferences concerning two populations_1 - 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online