could you help giving me explanations on this problem ? Thank you .

Except part (c)

Pleas use R/Rstudio !!!!

I The response time in milliseconds was determined for three different types of circuits that could he 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 1 9 12 10 3 15 2 20 21 23 1'? 30 3 6 5 8 16 7 (a) Test the hypothesis that the three circuit types have the same response time. Use or = 0.01. (b) Use Tukey's test to compare pairs of treatment means. Use or = 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 satised