# HW 5 Solution - Statistics 106 Homework 5 Solutions Due Nov...

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Statistics 106 Homework 5 Solutions Due : Nov. 7, 2016, In Class 19.5 In a two-factor study, the treatment means μ i j are as follows: Factor B Factor A B 1 B 2 B 3 B 4 A 1 250 265 268 269 A 2 288 273 270 269 a. Obtain the factor B main e ff ects. What do your results imply about factor B ? b. Prepare a treatment means plot and determine whether the two factors interact. How can you tell that interactions are present? Are the interactions important or unimportant? c. Make a logarithmic transformation of the μ i j and plot the transformed values to explore whether this transformation is helpful in reducing the interactions. What are your findings? Solution:
b. The treatment means plot is shown below: 1
c. The transformed treatment means plot is shown below: 2
19.8 Refer to Problem 19.5. Assume that σ = 4 and n = 6. 1. Obtain E { MS E } and E { MS AB } . 2. Is E { MS AB } substantially larger than E { MS E } ? What is the implication of this? Solution:
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b. E { MS AB } is substantially larger than E { MS E } . This implies it is very likely that the interaction e ff ects are present. 19.12 Eye contact e ff ect. In a study of the e ff ect of applicant’s eye contact (factor A ) and personnel o ffi cer’s gender (factor B ) on the personnel o ffi cer’s assessment of likely job success of applicant, 10 male and 10 female personnel o ffi cers were shown a front view photograph of an applicant’s face and were asked to give the person in the photograph a success rating on a scale of 0 (total failure) to 20 (outstanding success). Half of the o ffi cers in each gender group were chosen at random to receive a version of the photograph in which the applicant made eye contact with the camera lens. The other half received a version in which there was no eye contact. The success ratings are saved in ”CH19PR12.txt”. a. Obtain the fitted values for ANOVA model. b. Obtain the residuals. Do they sum to zero for each treatment? c. Prepare aligned residual dot plots for the treatments. What departures from ANOVA model can be