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# Determining null and alternative hypotheses The records of a casualty insurance company show that, in the past, its clients have had a mean of auto...

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A coin-operated coffee machine made by BIG Corporation was designed to discharge a mean of ounces ounces of coffee per cup. If it dispenses more that that on average, the corporation may lose money, and if it dispenses less, the customers may complain.

Believing that the mean amount of coffee dispensed by the machine, , is different from ounces, BIG plans to do a statistical test of the claim that the machine is working as designed. Technicians gather a random sample of fill amounts and find that the mean of the sample is ounces and that the standard deviation is ounces.

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1. Determining null and alternative hypotheses The records of a casualty insurance company show that, in the past, its clients have had a mean of auto accidents per day with a standard deviation of . The actuaries of the company claim that the standard deviation of the number of accidents per day is no longer equal to . Suppose that we want to carry out a hypothesis test to see if there is support for the actuaries' claim. State the null hypothesis and the alternative hypothesis that we would use for this test. The correct answer is: 2. Type I and Type II errors Some college graduates employed full-time work more than hours per week, and some work fewer than hours per week. We suspect that the mean number of hours worked per week by college graduates, , is greater than hours and wish to do a statistical test. We select a random sample of college graduates employed full-time and find that the mean of the sample is hours and that the standard deviation is hours. Based on this information, answer the questions below. The correct answer is:
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