You are manager of maintenance programs at a regional airline. You are looking at data from the last

nine Pratt &Whitney PW$-120$ engines to go through hot section overhaul. You notice that these

overhaul times or $$times between hot section overhaul$($TBHO$)$ vary considerably from one engine to

another, with the shortest TBHO at $950$ hours and the longest at $2850$ hours. You wonder if there might

be a correlation between the number of hot starts an engine experiences in its service life and the

duration that the engine remains in service without performance deterioration beyond limits$,$ measured

by the time between overhauls. This idea seems reasonable since engines experiencing overtemperature on startup can be very damaging and may lower engine TBHO.

You know that hot starts are recorded in the aircrafts log book on a daily basis so this information is

readily available in the airline$$s records system. You do your analysis and report your findings to your VP

of maintenance in the form of a memo. Include a discussion of correlation, what it is and how it can be

used to predict engine TBHO based on the number of hot starts an engine experiences in operation.

Also include an example of your analytical capability by informing your boss what TBHO to expect for an

engine that experiences zero hot starts and compare that to the TBHO of an engine that experiences $4$

hot starts.

# Hot Starts $12\mathrm{.}52344\mathrm{.}555\mathrm{.}56$

TBHO $24002000285028001600170014901100950$

In your analysis you notice something else. The established average hot section overhaul time

$($according to P&W technical publications$)$ for the fleet of PW$-120$ engines has been $2500$ hours. How

does this established TBHO compare to your sample of nine?

You decide to test the claim that the mean TBHO is $2500$ hours using a significance level of $5\%.$ What

are your findings. Report this in your memo as well. How does your airline$$s overhaul times measuring

up to the established norm?