Question

The National Institute of Standards and Technology (NIST) supplies "standard materials" whose physical properties are supposed to be known. For example, you can buy from NIST an iron rod whose electrical conductivity is supposed to be 10.1 at 293 kelvin. (The units for conductivity are microsiemens per centimeter. Distilled water has conductivity 0.5.) 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 of all measurements of the same rod has the Normal distribution with mean μ equal to the true conductivity and standard deviation σ = 0.1. Here are six measurements on the same standard iron rod, which is supposed to have conductivity 10.1.

10.06    9.87    10.04    10.12    10.21    10.11

NIST wants to give the buyer of this iron rod a 90% confidence interval for its true conductivity. What is this interval? (Round your answers to three decimal places.)

Answer 1

Sample mean = (10.06 + 9.87 + 10.04 + 10.12 + 10.21 + 10.11) / 6 = 10.06833

Since we know the population standard deviation σ, we will use z statistic for the 90% confidence interval.

Z value for 90% confidence interval is 1.645

Standard error of mean = σ / = 0.1 / = 0.0408

Margin of error = Z * Std error = 1.645 * 0.0408 = 0.067116

90% confidence interval is,

(10.06833 - 0.067116, 10.06833 + 0.067116)

(10.00121,  10.13545)