HW9Solutions

# HW9Solutions - 3. a. b. H o : = 1300 v. H a : > 1300 x is...

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

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

View Full Document
3. a. 1300 : = μ o H v. 1300 : > a H b. x is normally distributed with mean ( ) = x E and standard deviation . 416 . 13 20 60 = = n σ When H 0 is true, ( ) 1300 = x E . Thus 26 . 1331 ( = x P α when H 0 is true) = () 01 . 33 . 2 416 . 13 1300 26 . 1331 = = z P z P c. When 1350 = , x has a normal distribution with mean 1350 and standard deviation 13.416, so 26 . 1331 ( 1350 < = x P β when ) 1350 = = 0808 . 40 . 1 416 . 13 1350 26 . 1331 = = z P z P d. Replace 1331.26 by c, where c satisfies 645 . 1 416 . 13 1300 = c (since . Thus c = 1322.07. Increasing ) 05 . ) 645 . 1 ( = z P gives a decrease in ; now ( ) 0188 . 08 . 2 1350 = = z P . e. 26 . 1331 x iff 416 . 13 1300 26 . 1331 z i.e. iff . 33 . 2 z 4. a. H 0 : 5 . 5 = v.. H a : 5 . 5 ; for a level .01 test, (not specified in the problem description), reject H 0 if either or 58 . 2 z 58 . 2 z . Since 58 . 2 33 . 3 075 . 5 . 5 25 . 5 = = z , reject H 0 . b. ( ) ( ) + Φ + + Φ = 075 . 1 . 58 . 2 075 . 1 . 58 . 2 1 6 . 5 1 ( ) ( ) 105 . 91 . 3 25 . 1 1 = Φ + Φ = c. 97 . 216 1 . 33 . 2 58 . 2 3 . 2 = + = n , so use n = 217. 5. a. Let X = the number of couples who lean more to the right when they kiss. If n = 124 and p = 2/3, then E[X] = 124(2/3) = 82.667. The researchers observed x = 80, for a difference of 2.667. The probability in question is P(|X – 82.667| 2.667) = P(X 80 or X 85.33) = P(X 80) + [1 – P(X 85)] = Bin(80;124,2/3) + [1 – Bin(85;124,2/3)] = 0.634. (Using a large- sample z -based calculation gives a probability of 0.610.) b. We wish to test H 0 : p = 2/3 v. H a : p 2/3. From the data, 645 . 124 80 ˆ = = p , so our test statistic is 124 / ) 333 (. 667 .

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.

## This note was uploaded on 09/06/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell.

### Page1 / 9

HW9Solutions - 3. a. b. H o : = 1300 v. H a : > 1300 x is...

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

View Full Document
Ask a homework question - tutors are online