Discuss the below:
Q: A door manufacturer wants to monitor the performance of a new painting process, which has been designed to apply paint with a mean thickness of 0.7mm, by detecting any departure from this target. One hundred doors will be randomly chosen from a day's production, and the thickness of paint on each of the 100 doors will be measured.
a) Explain how you would test whether the mean thickness of paint on the entire day's production meets the required standard of 0.7mm, using a .01 level of significance. Include all the following in your explanation:
i) whether the test will be one-tailed or two-tailed;
ii) how you would calculate a test statistic;
iii) how you would define the rejection region;
iv) any assumptions you would make;
v) how you would interpret the possible results of the test.
b) Suppose the mean thickness of paint on the 100 doors tested is 0.65mm and the standard deviation is .02mm. Use these data to conduct the test of hypothesis