Question

3.22. The response time in milliseconds was determined for three different types of circuits that could be used in an auto- matic valve shutoff mechanism. The results from a complete- ly randomized experiment are shown in the following table: Circuit Type Response Time 10 23 12 15 30 20 21 17 16 (a) Test the hypothesis that the three circuit types have the same response time. Use α-0.01. (b) Use Tukey's test to compare pairs of treatment means Use a 0.01 (c) Use the graphical procedure in Section 3.5.3 to com- pare the treatment means. What conclusions can you draw? How do they compare with the conclusions from part (b)? (d) Construct a set of orthogonal contrasts, assuming that at the outset of the experiment you suspected the response time of circuit type 2 to be different from the other two (e) If you were the design engineer and you wished to minimize the response time, which circuit type would you select? (f) Analyze the residuals from this experiment. Are the basic analysis of variance assumptions satisfied?

Please use SAS to solve and show the code thank you.

Answer 1

a)

H0 : μ1 = μ2 = μ3

H1 : at least one mean is different

Source	DF	Sum of squares	Mean square	F-vale	Pr >F
Model	2	543.6000000	271.8000000	16.08	0.0004
Error	12	202.8000000	16.9000000
Corrected total	14	746.4000000

From the SAS output above, the calculated F statistic is F=16.08 with 2 and 12 degrees of freedoms. The corresponding P-value is 0.0004 which is less than $\alpha$ = 0.01, so there is at least one circuit type that is different.

As per HomeworkLib policy we need to solve four sub parts per question. Please post the remaining questions in another post.