(a) The surface roughness of ground product has a normal distribution with mean of 2.5um and standard deviation of 0.5 um. A journal reported that by adding nano carbon particle into the cutting lubricant, the roughness can be reduced. Radom sample of 40 products were tested and the mean roughness was 2.0 um. (i) Explain the Type 1 error and Type 2 Error. Identify the null and alternate hypothesis (ii) Test the claim at 5% level of confidence coefficient