An engineer who suspects that the surface finish of metal parts is influenced by the type

of the paint used and drying time. He selected three drying times $20,25,$ and $30$ minutes

and used two types of paint. Three parts are tested and the data as follows:

a$)$ State the appropriate hypotheses using the analysis of variance?

b$)$ Construct ANOVA table?

c$)$ Does paint type affect the surface finish? Explain.

d$)$ Does drying time affect the surface finish? Explain

e$)$ Do Paint type and drying time interact? Hint :Plot the interaction plots

Known that it is particularly important for a supermarket to reasonably employ cashier

staff, reduce customers' waiting time and the operating costs of the supermarket and

improves efficiency. Waiting time and customer dissatisfaction has a proportional

relationship.

Suppose that a store manager such as LULU Hypermarket would like to perform an

experiment on the waiting time. He defines the $($Waiting time $=$ waiting time until reach the

cashier $+$ service time at the cashier$).$ Use the context of DOE to help the manager improve

the waiting time. Your answer should be in the following sequential approach

a$)$ Before the experiments $($ Setting up the experiment, important factors $,$levels...etc$)$

e$.$g$.$ cashier experience

b$)$ During The experiments $($ how would you run the experiment$)$

c$)$ Data Collection $($noise$,$ errors...etc$)$

d$)$ Analysis of the results $($ list of necessary statistical tests$-$ plots...etc$)$

e$)$ Types of Conclusion $($ effects of factors....etc$)$