Assignment 6 sol

Assignment 6 sol - The University of Hong Kong Department...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
The University of Hong Kong Department of Statistics and Actuarial Science STAT0302 Business Statistics Semester 2 2008/2009 Assignment 6 Suggested Solution Q1. CHI-SQUARED TEST OF INDEPENDENCE: H F L P Total A 5 10 11 14 40 O 14 16 16 12 58 U 10 7 4 4 25 Total 29 33 31 30 123 0 H : Appearance is INDEPENENT of academic performance. A H : The two factors are NOT independent. Test statistic ( Under ): 0 H 2 ) 1 )( 1 ( 2 2 ~ } 1 . { = ∑∑ c r ij j i ij t s o n χ where and are the row and column totals for each observation . i s j t 97224 . 8 2 = Tables : Look up – tables: df = (r-1)(c-1)=2x3=6, since r=3 and c=4 2 α = 0.05 one-tailed which gives 12.59 as the critical value. Conclusion: Since the test statistic value 8.97224 is clearly < the critical value = 12.59 we DO NOT REJECT at the α = 5% level of significance. Hence, there is no relationship between a student’s academic performance and their appearance. 2 6 0 H
Background image of page 1

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

View Full DocumentRight Arrow Icon
Q2. USE TWO METHODS *********** Let , and be the proportion of voters favouring the legislation of low, average and high incomes respectively. A p B p C p 7 . 0 150 105 ˆ = = A p , 6 . 0 160 96 ˆ = = B p and 42 . 0 100 42 ˆ = = C p 6484 . 0 310 201 ˆ = = AB p , 588 . 0 250 147 ˆ = = AC p and 5308 . 0 260 138 ˆ = = BC p i) Hypothesis : 0 : 0 : 0 = = B A B A A B A B A p p p p H p p p p H Test statistic: ) 1 , 0 ( ~ ) 1 1 )( ˆ 1 ( ˆ ) ( ) ˆ ˆ ( N n n p p p p p p Z B A AB AB B A B A + = 8428 . 1 ) 160 1 150 1 )( 3516 . 0 )( 6484 . 0 ( 0 6 . 0 7 . 0 = + = Tables: Look up 0.475 in z – tables which gives 1.96 as the critical value. Conclusion: Since the test statistic value Z = 1.8428 < the critical value z = 1.96, so we DO NOT REJECT at the α = 5% level of significance. Hence, among low incomes and average incomes classes, the proportions of voters favouring the legislation are the same. 0 H ii) Hypothesis: 0 : 0 : 0 = = C A C A A C A C A p p p p H p p p p H
Background image of page 2
Test statistic: ) 1 , 0 ( ~ ) 1 1 )( ˆ 1 ( ˆ ) ( ) ˆ ˆ ( N n n p p p p p p Z C A AC AC C A C A + = 4065 . 4 ) 100 1 150 1 )( 412 . 0 )( 588 . 0 ( 0 42 . 0 7 . 0 = + = Tables: Look up 0.475 in z – tables which gives 1.96 as the critical value. Conclusion: Since the test statistic value Z = 4.4065 > the critical value z = 1.96, so we REJECT at the α = 5% level of significance. Hence, among low incomes and high incomes classes, the proportions of voters favouring the legislation are not the same. 0
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 19

Assignment 6 sol - The University of Hong Kong Department...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online