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1. A medical laboratory claims that the mean turn-around time for performance of a battery of tests on blood samples is less than 2 business days. However, the manager of a large medical practice believes that the actual mean is larger. A random sample of 45 blood samples yielded a mean of 2.09 business days and a sample standard deviation 0.13 days. Perform the relevant test to see if there is support for the manager's belief at the 10% level of significance, using these data. Without using technical terms, explain all of your results of this test to the manager.
2. The government of an impoverished country reports the mean age at death among those who have survived to adulthood as 66.2 years but a relief agency believes that the actual age is less than this. To determine whether the age at death is, in fact, less than 66.2 years, a random sample of 30 deaths was examined and resulted in a mean of 62.3 years. Test whether these data support the belief of the relief agency, assuming that the population standard deviation is 8.1 years and that the agency is willing to make a Type 1 error 1% of the time. Interpret your results in the context of this problem.