Question

14-4) The National Institute of Standards and Technology (NIST) supplies “standard materials” whose physical properties are supposed to be known. For example, you canbuy from NIST a liquid whose electrical conductivity is supposed to be 5. (The units for conductivity are microsiemens per centimeter. Distilled water has conductivity0.5.) Of course, no measurement is exactly correct. NIST knows the variability of its measurements very well, so it is quite realistic to assume that the population ofall measurements of the same liquid has the Normal distribution with mean µ equal to the true conductivity and standard deviation s = 0.2. Here are 6 measurements onthe same standard liquid, which is supposed to have conductivity 5:

5.32 4.88 5.10 4.73 5.15 4.75

NIST wants to give the buyer of this liquid a 90% confidence interval for its true conductivity. What is this interval?

Answer 1

Since we know the population standard deviation, we can use a z confidence interval. For a 90% confidence interval, z* = 1.645

The standard error is given with:

So we have

Our margin of error is given by

Since

Our interval is

Answer 2

oh~