5. An experiment was run to determine whether different colored candles (red, white, blue, yellow) burn at

different speeds. Each experimenter collected four observations on each color in a random order, and

"experimenter" was used as a blocking factor. The design was a general complete block design with V=

4, k = 16, b = 4, and s=4. The resulting burning times (in seconds) are shown in Table 17.21 in the

book and can be downloaded at http://deanvossdraguljic.ietsandbox.net/DeanVossDraguljic/SAS-

data/candle.sas.

(a)Analyze the experiment as though the experimenters represent a random sample from a large population

of people who might use these candles in practice. Use a two-way mixed model with interaction where

the experimenters are blocks with random effects and the interactions of block and color are random as

well. The color has fixed effects. Provide the 95% simultaneous confidence intervals for all pairwise

comparisons of color using Tukey's method.

(b)Provide the SAS code for 1(a).

(c)In 1(a), suppose we do not treat these experimenters as a random sample from a large population and

consequently the model does not have random effects. Provide the 95% simultaneous confidence intervals

for all pairwise comparisons of color using Tukey's method.

(d)Provide the SAS code for 1(c)

(e)Which model provides shorter confidence intervals? Give a justification if you could.

(f)If a two-way main-effects model was used in 1(a) and 1(c), do you think the two models (one with random

effects and one without) would produce the simultaneous confidence intervals of different lengths?