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# Statistics - Hypothesis Testing and Type 2 Error

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A corporation owns a factory that produces sulfuric acid. Because of changing
conditions, the plant's output is quite variable. The company's president has observed that the output is normally distributed with a mean of 8,200 pieces per hour. He recently has been informed that the government is considering a new law that would require him to alter the way in which the acid is produced. He reorganizes production facilities to comply and observes the hourly output for two working days (16 hours). At a 5% significance level do these data indicate that the new guidelines will reduce output? The
data are shown below:

8,283
8,121
7,905
8,097
7,969
8,101
8,069
8,240
8,410
8,483
8,510
7,480
8,097
8,237
7,682
8,076

An employee at the company believes that production has really gone down to 8000 Liters per hour, which represents a true reduction of output and is surely a possible value supporting the alternative hypothesis. Find the probability that the statistician makes an error of Type 2 - ie that the true mean is really 8000 L per hour but yet we accept the null hypothesis.