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4. Consider 26-3 fractional factorial design with the generators 12 , 5 23 , and 6 = 123. Assume that third- and higher-order interaction effects are negligible(a) ...

Question

4. Consider 26-3 fractional factorial design with the generators 12 , 5 23 , and 6 = 123. Assume that third- and higher-order interaction effects are negligible(a) Display the linear combinations of effects that can be estimated from this design_(b) The experimental results in part (a) were somewhat ambiguous; therefore, a second fractional factorial design, the mirror image design, is to be performed_ What are the generators for one possible mirror image? Display the linear combinations of effe

4. Consider 26-3 fractional factorial design with the generators 12 , 5 23 , and 6 = 123. Assume that third- and higher-order interaction effects are negligible (a) Display the linear combinations of effects that can be estimated from this design_ (b) The experimental results in part (a) were somewhat ambiguous; therefore, a second fractional factorial design, the mirror image design, is to be performed_ What are the generators for one possible mirror image? Display the linear combinations of effects that can be estimated from this mirror image design (c) When these two designs are combined, what effects, or linear combinations of effects_ can be estimated?



Answers

A pair of dice is rolled 500 times with the following frequencies: $$\begin{array}{lrrrrrrrrrrr}\text { Sum } & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 \\\text { Frequency } & 11 & 35 & 44 & 50 & 71 & 89 & 72 & 52 & 36 & 26 & 14\end{array}$$ (A) Compute the approximate empirical probability for each outcome. (B) Compute the theoretical probability for each outcome, assuming fair dice. (C) Compute the expected frequency of each outcome. (D) Describe how a random number generator could be used to simulate this experiment. If your graphing utility has a random number generator, use it to simulate 500 tosses of a pair of dice and compare your results with part C.

The given question is Burt Baskin and I are Vero Bins began making ice cream in 1945. Initially, there developed 31 flavors, one for each day off the month. There is three part off this question in part A. How many 20 points are possible using the 31 original flavours? If order or flavor is to be considered and no flavor is repeated now by using convict by using permutation formula here we get 31 fact O'Ryan to fact O'Ryan. They're divine, minus defacto. Get 31 factorial divided by 31 minus two. Factorial, we get 31 factorial divided by 29 factorial. By solving it, we get 9 30 in part B. How many toe dip cones are possible if order is to be considered on, the flavor can be repeated. You flavor can be debris. Dude becomes 31 in tow. 31 is E questo 961 in Part C. How many total concert possible? If order is not considered and no flavor is repeated by using combination formula. Here we get 31 factorial divided by two factorial in tow, 31 miles minus two. Factorial, we get 30 Van Factorial divided by two factorial into 29 Factorial. By solving it, we get 4 65 This is the answer.


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