3044hw4s09sols

# 3044hw4s09sols - E i = 10, the following table is...

This preview shows pages 1–2. Sign up to view the full content.

2 ISyE 3044/Spring 2009/Solutions to Exercises 3-4 from Homework #4 2. (a) We have the following table interval i [0 , 0 . 25) [0 . 25 , 0 . 50) [0 . 50 , 0 . 75) [0 . 75 , 1) O i 2 7 7 3 E i 5 5 5 5 The test statistic is χ 2 0 = (2 - 5) 2 5 + (7 - 5) 2 5 + (7 - 5) 2 5 + (3 - 5) 2 5 = 21 5 = 4 . 2 . Since χ 2 0 χ 2 3 , 0 . 10 = 6 . 25, we fail to reject H 0 . (b) The multipliers are a = 2 , 6 , 7 , 8. For each of these multipliers, verify that the smallest integer k such that a k - 1 is divisible by m = 11 is k = m - 1 = 10. (See page 255 of the text.) 7.4 X 0 = 27 , a = 8 , c = 47 , m = 100. X 1 = (8 × 27 + 47)mod 100 = 63 , R 1 = 63 / 100 = . 63. X 2 = (8 × 63 + 47)mod 100 = 51 , R 2 = 51 / 100 = . 51. X 3 = (8 × 51 + 47)mod 100 = 55 , R 3 = 55 / 100 = . 55. 7.8 Let ten intervals be de±ned each from (10 i - 9) to (10 i ) where i = 1 , 2 ,..., 10. By counting the numbers that fall within each interval and comparing this to the expected value for each interval,

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: E i = 10, the following table is generated: Interval O i ( O i-E i ) 2 /E i (01-10) 9 0.1 (11-20) 9 0.1 (21-30) 9 0.1 (31-40) 6 1.6 (41-50) 17 4.9 (51-60) 5 2.5 (61-70) 10 0.0 (71-80) 12 0.4 (81-90) 7 0.9 (91-00) 16 3.6 100 14 . 2 = χ 2 3 From Table A.6, χ 2 . 05 , 9 = 16 . 9. Since χ 2 < χ . 05 , 9 , then the null hypothesis of no di±erence between the sample distribution and the uniform distribution is not rejected. 7.10 X 1 = [7 × 37 + 29] mod 100 = 88 and R 1 = . 88. X 2 = [7 × 88 + 29] mod 100 = 45 and R 2 = . 45. X 3 = [7 × 45 + 29] mod 100 = 44 and R 3 = . 44....
View Full Document

## This note was uploaded on 09/17/2009 for the course ISYE 3044 taught by Professor Alexopoulos during the Spring '08 term at Georgia Institute of Technology.

### Page1 / 2

3044hw4s09sols - E i = 10, the following table is...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online