A paper manufacturer has a production process that operates continuously through

Question

A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 8 inches, and the standard deviation of the length is 0.04 inch. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 8 inches or whether something has gone wrong in the production process to change the length of the paper produced. A random sample of 100 sheets is selected, and the mean paper length is inches. A 99% confidence interval estimate for the population mean paper length is 7.99168 lessthanorequalto mu lessthanorequalto 8.01232. Is it true that you do not know for sure whether the population mean is between 7.99168 and 8.01232 inches? Explain. Choose the correct answer below. It is false because the sample mean falls outside the interval. It is true because the population mean will be in the interval only 1% of the time. It is false because the sample mean falls within the interval. is true because the population mean will be in the interval only 99% of the time.

Explanation / Answer

Expected mean leangth of paper = 8 inches

standerd deviation = 0.04 inch

N = 100; Mean found = 8.002 inch

99% confidence inteval estimate paper length is 7.99168 <=   <= 8.01232

so the sample mean of 8.002 inch has been found in between the 99% confidence interval.

so option a and option b has been cancelled out because both are wrong statement.

Option c seems legit as we know that there is 99% chances that mean will lie in the given interval but we can't be 100% sure about that.

The problem is of Normal DIstribution so the population mean can not be derived exactly or can't be tell for sure because it can include some outliers.

so Option D is the right answer that it is true that we don't know for sure that the population mean is between interval, because it is only 99% time that population mean is in interval.

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