Please work on this assessment individually. You can use books, internet, or your notes, but please do not give or receive help to/from your fellow students. This time I am just looking for short answers, not a nice report format.
1. Your company gets a report in which effects of factors A and B on company sales were evaluated. The design used 10 stores as the blocks and factor A was at 3 levels, factor B at two. This table was included in the report where the 2 rows indicate the 2 levels of B and the three columns indicate the 3 levels of A.
80 / 75 / 5550 / 85 / 65
The report also gave the estimated variances as follows (it seems they use SAS!):
Covariance Parameter
Estimates
Cov Parm Estimate
store 1263.11
Residual 341.33
(A) How many observations were in the original experiment?
(B) Your boss asks you to put a 95% confidence interval on the difference of the B effects at the low level of factor A (50-80=-30, a drop of 30 in sales). What numerical value would you use as the standard error for that confidence interval?
(C) Fill in the missing numerator and denominator degrees of freedom for F in the following analysis of fixed effects (hint: answer is the same whether GLM or MIXED was used):
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
A __ __ 6.35 0.0037
B __ __ 0.49 0.4883
A*B __ 45 7.81 0.0012
(D) Your boss is especially interested in what mean sales would be for the low level of both factors (table, top left corner) which is estimated to be 80 as you see. What is the standard error for this sample average? (give the numerical value)
(E) Your boss also suggests that there is no reason to be concerned with factor B, based on the insignificant F test for B in the table above. He says to just report the 3 A means averaged over the two levels of B. What concerns do you have regarding this suggestion and why?
(F) Why is it that the calculation for part (D) involves the store variance estimate 1263 while the calculation for (B) does not? (yes, I know this gives you a hint for B and D)
2. Here are the design points for a central composite design in 2 variables X1 and X2, standardized so that the box part has coordinates that are all -1 and 1 and using 1.5 as the axial distance and 3 center points.
(A) Fill in the missing design points (add more blanks if needed):
X1 X2
0 0
0 0
0 0
0 1.5
1.5 0
-1 1
1 -1
1 1
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(B)I will now fit a full quadratic model to the data (no blocks here). How many error degrees of freedom will I have?
3. I have a 28 factorial set of treatments, with factors A, B, C, D, E, F, G, H which is too many treatment combinations to run. As usual I define the two levels of each factor to be -1 and 1. I decide to run only the treatment combinations in which the product ABCD is 1 and DEFG is also 1. How many combinations will I have to run? Write out the defining contrast for this fractional factorial treatment arrangement. What are the three aliases of the AD interaction?
By my typed or signed signature, I verify that I have neither given nor received help from other class members on this assessment
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(signature signed or typed)