A 15-minute Oil and Lube service claims that their average service time is no ...

     1. A 15-minute Oil and   Lube service claims that their average service time is no more than 15   minutes. A random sample of 40 service times was collected, and the sample   mean was found to be 16.4 minutes, with a sample standard deviation of 3.2   minutes. Is there evidence to support, or to reject the claim at the alpha =   0.01 level? Perform an appropriate hypothesis test, showing the necessary   calculations and/or explaining the process used to obtain the results 

2.      An engineering firm   is evaluating their back charges. They originally believed their average back   charge was $1800. They are concerned that the true average is higher, which   could hurt their quarterly earnings. They randomly select 40 customers, and   calculate the corresponding sample mean back charge to be $1950. If the   standard deviation of back charges is $500, and alpha = 0.01, should the   engineering firm be concerned? Perform an appropriate hypothesis test,   showing the necessary calculations and/or explaining the process used to   obtain the results    

3.      A drug manufacturer   wants to estimate the mean heart rate for patients with a certain heart   condition. Because the condition is rare, the manufacturer can only find 18   people with the condition currently untreated. From this small sample, the   mean heart rate is 93 beats per minute with a standard deviation of 6.   (a) Find a 98% confidence interval for   the true mean heart rate of all people with this untreated condition. Show   your calculations and/or explain the process used to obtain the interval.   (b) Interpret this confidence interval   and write a sentence that explains it.