(a) The surface roughness of ground product has a normal distribution with mean of 2.5µm and standard deviation of 0.5 µm. 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 µm. (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.
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(a) The surface roughness of ground product has a
and standard deviation of 0.5 µm. 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 µm.
(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.
(b) In the same situation as Q2 (a), line engineers claim that cutting tool vibration give
effect to the surface roughness results. After the cutting worn out and replaced, grinding
process was done on a batch of product. Random sample of 20 products was inspected
and the mean roughness was 2.2µm.
(i) Identify the hypothesis for this situation.
(ii) Test the claim using 95% level of significant.
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