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