Exercise4.1 The advertisementofthefastfoodchainofrestaurants“FastBurger”claimsthatthe averagewaitingtimeforfoodinitsbranchesis30secondsunlike50secondsoftheircompetitors.

Mr.Skepticdoesnotbelievemuchinadvertisinganddecidedtotestitstruthbythefollowingtest:
he willgotooneof“FastBurger’s”branches,measurethewaitingtimeandifitislessthan40 seconds (thecriticalwaitingtimehefixed)hewouldbelieveinitsadvertisement.Otherwise,he wouldconcludethattheservicein“FastBurger”isnofasterthaninotherfastfoodcompanies.Mr.
Skepticalsoassumesthatwaitingtimeisexponentiallydistributed.
1. What arethehypothesesMr.Skeptictests?Calculatetheprobabilitiesoferrorsofbothtypesfor his test.
2. Can yousuggestabettertesttoMr.Skepticwiththesamesignificancelevel?
3. Mrs. Skeptic,Mr.Skeptic’swife,agreesingeneralwiththetestherhusbandhasusedbutdecided instead tofixacriticalwaitingtimethatwillminimizethesumoftheprobabilitiesofbotherror types. Whatwillbehercriticalwaitingtime?
4. Calculate theprobabilitiesoftheerrorsforMrs.Skeptic’stestandcomparethemwiththoseof her husband.