CPSC_440_Quiz_14_GF

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School

University of Illinois, Urbana Champaign *

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440

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Statistics

Date

Jan 9, 2024

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pdf

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Uploaded by dfhuber

1 Name: TA: Lab section: CPSC 440 – Quiz 14 1. (6 points) A biologist is interested in directly comparing the fertility of t = 4 different lines of mice. They want to see if the population mean of Line 3 is more fertile than the population means of Lines 1, 2, and 4. Each mouse line has ࠵? = 10 mice, resulting in a total sample size of N = 40. a. (1 point) Set up an appropriate linear combination for this comparison: ࠵? = ࠵? ! − ࠵? " + ࠵? # + ࠵? $ 3 b. (1 point) Is this a contrast? Justify your answer mathematically. Yes, the coefficient 1+(-1/3)+(-1/3) +(-1/3)=0 c. (2 points) What are the appropriate null and alternative hypotheses to test the biologist’s question? ࠵? % : ࠵? ≤ 0 ࠵?࠵?. ࠵? & : ࠵? > 0 d. (2 points) Please find the appropriate ࠵? = 0.05 critical value. Df MSE=N-t=40-4=36 > qt(0.95,36) [1] 1.688298 ࠵? ’()* = ࠵? +.+-,!/ = 1.69

2 2. (2 points) Immediately below is an ANOVA table for an RCBD model. The second ANOVA table is for a model where the “Block” factor was removed. Please fill in the second table. Source df Sum Sq Mean Sq F Value Treatment 2 48.17 24.09 9.17 Block 2 6.16 3.08 1.17 Residuals 4 10.51 2.63 Total 8 64.84 DF Sum Sq Mean Sq F Value Treatment 2 48.17 24.09 8.67 Residuals 6 16.67 2.78 Total 8 64.84 3. (2 points) A physicist is interested in finding whether there is a linear relationship between the particle momentum ( x ) and its kinetic energy ( Y ). They collected data for N =90 trials: ࠵? ! ࠵? ! (࠵? ! − ࠵?̅) (࠵? ! − ࠵? ’ ) (࠵? ! − ࠵?̅)(࠵? ! − ࠵? ’ ) (࠵? ! − ࠵?̅) " (࠵? ! − ࠵? ’ ) " Sum 0.950 1.124 0.075 0.254 0.098 0.108 0.605 Mean 0.160 0.145 0.134 0.856 1.024 0.650 1.495 a. (2 points) Please find the least squares estimates ࠵? 7 + and ࠵? 7 " . ࠵? ) = ࠵? + + ࠵? " ࠵? ) + ࠵? ) df. 90 1 1 88 ࠵? ) = kinetic energy of the ࠵? *0 trial ࠵? + = the intercept parameter ࠵? " = the slope parameter ࠵? ) = the particle momentum of the ࠵? *0 trial ࠵? ) = the error term showing the variability in the kinetic energy that is not explained by the linear relationship with the particle momentum of the ࠵? *0 trial ~NID ( 0, ࠵? # ) (df=90- 2=88) Sxy=0.098 Sxx=0.108

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