hw4sol - Stat 511 Homework 4 Solution Spring 2011 up...

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

View Full Document Right Arrow Icon
Stat 511 Homework 4 Solution Spring 2011 1. Last HW had the β vector and X matrix for a very messed up experiment. They were: μα 1 α 2 α 3 α 4 α 5 α 6 1 101100 1 100100 1 110011 1 111011 1 100000 1 000000 1 001011 1 1 The X matrix and data, y , are in the Fle ’messedup.txt’ on the class web site. (a) Estimate a 90% conFdence interval for α 4 ( α 2 + α 5 + α 6 ). The corresponding C is C =(0 , 0 , 1 , 0 , 1 , 1 , 1), thus the 90% C.I is c ± t 3 , 95% p ± σ 2 C ( X 0 X ) C 0 =[0 . 7896 , 2 . 9104] (b) Test Ho: α 1 =0. (N .B . α 1 is estimable). Report your test statistic and p-value. The corresponding C is C , 1 , 0 , 0 , 0 , 0 , 0), thus the test statistic T is T = c d p ± σ 2 C ( X 0 X ) C 0 =1 . 7259 , thus the p-value is P ( | t 3 | >T )=0 . 1828, fail to reject the null hypothesis α 1 =0 . (c) Test Ho: α 1 2 4 , and α 5 + α 6 = 0. (N.B. This hypothesis is testable) Report your test statistic and p-value. The corresponding C is C = 0100000 0010000 0000100 0000011 with full rank 4 and the test statistic ± is F = ( c d ) 0 ( C ( X 0 X ) C 0 ) 1 ( c d ) / 4 ± σ 2 =32 . 7214 The p-value is P ( F 4 , 3 >F . 008, then we reject the null hypothesis, namely, at least one of α 1 2 4 , and α 5 + α 6 is not zero. 2. This problem is based on a research proposal I read last week. A researcher on campus is studying whether monkeys are selective in what they eat. One of the major items in the diet 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
Stat 511 Homework 4 Solution Spring 2011 of a particular group of monkeys is the fruit of the baobab tree. The researcher is measur- ing various nutrient characteristics of the baobab fruits. One of the most important is the sugar concentration. This is not easy to measure and even harder to measure precisely. The researcher wanted to estimate the precision of her method of determining baobab sugar con- centration. There are no standard reference materials (samples with known chararacteristics) for baobab fruits, so the measurement error has to be estimated from multiple measurements on the same fruits. The researcher collected 8 fruits and measured each twice. (Ask if you don’t remember how to estimate measurement variance from this sort of data). The data are in baobab.txt on the class web site.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 6

hw4sol - Stat 511 Homework 4 Solution Spring 2011 up...

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

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