hw6-solution.pdf

# Discuss b conduct separate tests for type of group

• Homework Help
• 10

This preview shows pages 4–7. Sign up to view the full content.

Discuss. b. Conduct separate tests for type of group and size of group main e ff ects. In each test, use level of significance α = . 01 and state the alternatives, decision rule, and conclusion. What is the P -value for each test? c. Obtain confidence intervals for D 1 = μ . 2 - μ . 1 , D 2 = μ . 3 - μ . 2 , and D 3 = μ . 4 - μ . 3 ; use the Bonferroni procedure with a 95 percent family confidence coe ffi cient. State your findings. d. Is the Bonferroni procedure used in pan (c) the most e ffi cient one here? Explain. Solution: a. The plot of the observations are shown below: 4

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

It appears that interaction e ff ects are very little, since the two curves are nearly parallel. Factor A main e ff ects are also very little, since the two curves are nearly overlapped. Factor B main e ff ects are present, since the two curves have large departure from horizontal. b. We first construct the ANOVA table. Note that the error sum of squares is given by S S AB , which can be obtained by S S AB = S S TO - S S A - S S B in R. Source S S d f MS Type of group 1.125 1 1.125 Size of group 318.375 3 106.125 Error 6.375 3 2.125 Total 325.875 7 F test for type of group main e ff ects: H 0 : α 1 = α 2 = 0, H a : not both α 1 and α 2 are 0. F * = MS A / MS AB = 1 . 125 / 2 . 125 = . 53, F (1 - α ; a - 1 , ( a - 1)( b - 1)) = F ( . 99; 1 , 3) = 34 . 1. If F * < 34 . 1, conclude H 0 , otherwise H a . Here conclude H 0 . P -value = .52. H 0 : β 1 = β 2 = β 3 = β 4 = 0, H a : not all β i ’s are 0. F * = MS B / MS AB = 106 . 125 / 2 . 125 = 49 . 94, F (1 - α ; b - 1 , ( a - 1)( b - 1)) = F ( . 99; 3 , 3) = 29 . 5. If F * < 29 . 5, conclude H 0 , otherwise H a . Here conclude H a . P -value = .005. 5
c. ˆ D 1 = ¯ Y . 2 - ¯ Y . 1 = 6, ˆ D 2 = ¯ Y 3 . - ¯ Y 2 . = 7 . 5, ˆ D 3 = ¯ Y . 4 - ¯ Y . 3 = 2 . 5. s ( ˆ D 1 ) = s ( ˆ D 2 ) = s ( ˆ D 3 ) = 2 MS AB / a = 1 . 4577. B = t (1 - α/ (2 g ); ( a - 1)( b - 1)) = t ( . 99167; 3) = 4 . 857. Thus, the 95% family-wise CI for D 1 , D 2 and D 3 using the Bonferroni procedure are 6 ± 4 . 857(1 . 4577) = [ - 1 . 08 , 13 . 08], 7 . 5 ± 4 . 857(1 . 4577) = [ . 42 , 14 . 58] and 2 . 5 ± 4 . 857(1 . 4577) = [ - 4 . 58 , 9 . 58]. d. Sche ff e’s procedure and Tukey’s procedure are also applicable in part (c). S = ( b - 1) F (1 - α ; b - 1 , ( a - 1)( b - 1)) = 3 F ( . 95; 3 , 3) = 5 . 275, T = 1 2 q (1 - α ; b , ( a - 1)( b - 1)) = 1 2 q ( . 95; 4 , 3) = 4 . 822. Since T < B < S , the Tukey’s procedure is the most e ffi cient in part (c). 21.7 Fat in diets. A researcher studied the e ff ects of three experimental diets with varying fat contents on the total lipid (fat) level in plasma. Total lipid level is a widely used predictor of coronary heart disease. Fifteen male subjects who were within 20 percent of their ideal body weight were grouped into five blocks according to age. Within each block, the three experimental diets were randomly assigned to the three subjects. Data on reduction in lipid level (in grams per liter) after the subjects were on the diet for a fixed period of time follow.

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

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern