10 May 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.
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