STAT XXXXXXXXXXHW#8
Due Date: 4/8/2020 (Thursday)
Homework must be submitted to Assignment #8 on Blackboard
On the top right corner, write your name, date, and HW #.
All problem numbers refer to the problem from Dean, Voss, and Dragulijic (DVD)
Please summarize your results from statistical software such as R or SAS
(DVD #10.5) Light bulb experiments
P. Bist, G. Deshpande, T.-W. Kung, R. Laifa, and C.-H. Wang ran an experiment in 1995 to compare the light intensities of three different
ands of light bulbs (coded 1, 2, 3), together with the effect of the percentage capacity (100% and 50%) of the bulb, the latter being controlled by a dimmer switch. Thus, there were v = 6 treatment combinations in total:
(100%, Brand 1) = 1, (100%, Brand 2) = 2, (100%, Brand 3) = 3, (50%, Brand 1) = 4, (50%, Brand 2) = 5, (50%, Brand 3) = 6.
Two blocks were used (one per day), with all 60 watt bulbs observed in one block, and all 100 watt bulbs in the other. Four observations were taken on each of the v = 6 treatment combinations in each block. The response variable was the observed resistance of a photo-resistor connected to the bulb, where high illumination co
esponds to low resistance. The data (resistances) are shown in Table 10.19.
(2 pts) Fit a block-treatment-interaction model to the data and calculate an analysis of variance table.
(2 pts) Show that the null hypothesis of no blockรtreatment interaction would be rejected at level ฮฑ = 0.005.
(2 pts) Calculate a set of confidence intervals for pairwise differences in the treatments for each block separately. Specify the method that you are using and the overall confidence level.
(2 pts) In terms of the six treatment parameters, write down two contrasts representing the interaction between
and and percentage capacity (averaged over blocks). Test whether these contrasts are significantly different from zero.
(2 pts) Suppose that the purpose of the experiment was to determine the best
and (in terms of illumination) for each percentage capacity and for 100 watt bulbs. Which
and(s) would you recommend and why?