RapidOilChange, Inc., an automotive tune-up shop, advertises that its personnel can, on average, carry out an oil change in 10 minutes or less. The Better Business Bureau received complaints from customers that it actually takes considerably longer to carry out an oil change at RapidOilChange. To check the company’s claim, the Better Business Bureau had the oil changed on 50 unmarked cars. The mean time it took for an oil change was 10.5 minutes, with a sample standard deviation of 1 minute.
Since 10.5 minutes is greater than the claimed value of 10 minutes, explain why we even need to carry out a hypothesis test.
At the level of significance of α = 0.01, carry out a hypothesis test to test RapidOilChange’s claim.