Please Answer ONLY part a but first complete all the 3 F-Tests and show steps to find out if there is Interaction between the two factors, the Type of Paint and Drying Time.

Then, please perform the required 3 Hypothesis Tests and include for each test the followings:

A Hypothesis test with the required 5 steps and use ONLY the Standard Rejection Rule for this test and give required plot

An engineer suspects that the surface finish of metal parts is influenced by the type of paint used and the drying time. He selected three drying times - 20, 25, and 30 minutes - and used two types of paint. Three parts are tested with each combination of paint type and drying time. The data are as follows: Drying Time (min) Paint 20 25 30 75 74 77 1 62 60 86 50 41 92 93 99 67 2 86 72 43 70 89 84 (a) State and test the hypotheses of interest in this experiment, and draw conclusions using the analysis of variance with a = 0.05. (b) Analyze the residuals from this experiment. significant, the interaction between the paint and drying time (a) The paint significant, the drying time significant. (b) The model assumptions reasonable. An engineer suspects that the surface finish of metal parts is influenced by the type of paint used and the drying time. He selected three drying times - 20, 25, and 30 minutes - and used two types of paint. Three parts are tested with each combination of paint type and drying time. The data are as follows: Drying Time (min) Paint 20 25 30 75 74 77 1 62 60 86 50 41 92 93 99 67 2 86 72 43 70 89 84 (a) State and test the hypotheses of interest in this experiment, and draw conclusions using the analysis of variance with a = 0.05. (b) Analyze the residuals from this experiment. significant, the interaction between the paint and drying time (a) The paint significant, the drying time significant. (b) The model assumptions reasonable