Problem $1$

Reference the "Process" tab in your data spreadsheet.

You are a manufacturer of outdoor picnic furniture $($benches$,$ picnic tables, litter receptacles, etc.$).$ You are

developing a new $($experimental$)$ manufacturing process. You have two process designs $($labeled Process $1$ and

Process $2$ in the data file$).$ The data you gathered is total cycle time in minutes. Faster is better. The goal is to do it

in less than $96$ minutes but if it cannot be done in less than $96$ minutes $($on average$)$ faster is still better. You have

run both processes on $15$ products.

Provide the p$-$value and confidence level for question $1,2,3,4,$ and $5.$ In addition, make sure to explain if the

Processes are different for questions $1,2,3,4,$ and $5,$ based on $90\%$ confidence level $($alpha $=10\%).$

Compare sample data for Process $1$ versus Process $2.$

Is the average cycle time of one Process faster than the other $($is Process $1$ faster than Process $2,$ or is Process $2$

faster than Process $1)?$

Is the $\%$ less than $96$ minutes for one Process less than the other $($is $\%$ less than $96$ minutes lower for Process $1$

than Process $2,$ or is $\%$ less than $96$ minutes lower for Process $2$ than Process $1)?$

Is the variation of one Process better than the other?

Assume the Process Design $($can be $1$ or $2,$ depending on your data set$),$ with the faster cycle time, will require a

significantly higher investment in new equipment versus the other. You need to be $97\%$ confident to make your

decision to invest in the faster, lower variation Process. Should you make the investment? Use your prior analyses.

Analyze whether the cycle time for the two Processes is different, lining up the data by experiment $($product$)$

number

Calculate the $95\%$ confidence interval of the average and $\%$ less than $96$ minutes for both Processes.