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# 1)For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.

1)For the following statement, write the null hypothesis and the alternative hypothesis. Then, label the one that is the claim being made.The mean life of a car’s engine is no more than 10 years2)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 = 0.04, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results3)A marketing firm wants to estimate the average amount spent by patients at the hospital pharmacy. For a sample of 70 randomly selected patients, the mean amount spent was $58.72 and the standard deviation $7.60.(a) Find a 90% confidence interval for the mean amount spent by patients at the pharmacy. 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.4)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 29 people with the condition currently untreated. From this small sample, the mean heart rate is 90 beats per minute with a standard deviation of 5.(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.5) The heights of 10 sixth graders are listed in inches: {54, 62, 54, 57, 60, 61, 53, 63, 59, 56}. (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?