Question

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 15 feet. It is known that the standard deviation in the cutting length is 0.2 feet. A sample of 60 cut sheets yields a mean length of 15.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. True or False: The confidence interval indicates t

Answer 1

False.

To construct a confidence interval for the mean length when the population standard deviation is known, you would typically use the z-distribution, not the t-distribution. In this case, since the sample size is large (n=60), the Central Limit Theorem justifies using the z-distribution, which is more appropriate due to the known standard deviation (0.2 feet).

For the 99% confidence level, you would look up the z-value associated with 99% in the z-table, which is approximately 2.576. The confidence interval can then be calculated using that z-value.

In summary, the statement is false because the confidence interval would use the z-distribution, not the t-distribution.