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 12 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 12 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 11.997 inches. A 95% confidence interval estimate for the population mean paper length is 11.98916 lessthanorequalto mu lessthanorequalto 12.00484. ls it true that you do not know for sure whether the population mean is between 11.98916 and 12.00484 inches? Explain. Choose the correct answer below. It is false because the sample mean falls within the interval. It is true because the population mean will be in the interval only 5% of the time. It is true because the population mean will be in the interval only 95% of the time. It is false because the sample mean falls outside the interval.

Explanation / Answer

95% Confidence interval means 95% of the times the mean of the selected sample will fall within the interval of (11.98916, 12.00484). Hence we can not state with 100% accuracy that the mean length of paper will fall within the given interval.

Hence option C is correct.
It is true because the population mean will be in the interval only 95% of the time

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