I'm working on a few confidence interval questions, each with slight differences that make it very hard to determine what to use.
One question asks:
An electric scale gives a reading equal to the true weight plus a random error that is normally distributed with mean 0 mg and standard deviation = 0.1 mg. Suppose that the results of five successive weighings (in mg) of the same object are as follows:
Heading 3.142, 3.163, 3.155, 3.150, 3.141 .
a) Compute a 95 percent confidence interval estimate of the true weight.
b) Compute a 99 percent confidence interval estimate of the true weight.
So here, the true mean is known. The standard deviation is known and all stats associated with the sample is known. What formula is used in this situation? The student-t? I tried but it's long and I think there's a faster way.
The other question asks:
Each of 16 science students independently measured the melting point of lead. The sample mean of these measurements was 330.2 degrees centigrade.
a) If the standard deviation of such measurements is known to be 14, find a 99 percent two sided confidence interval estimate of the true melting point of lead.
b) Suppose that the population variance is not known in advance. If the sample standard deviation is 15.4 degrees centigrade, compute a 99 percent two-sided confidence interval of the true melting point of lead.
In one situation we have the Standard Deviation, in the other we only have the sample standard deviation. What is used here?