The National Institute of Standards and Technology (NIST) supplies \"standard ma

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 equal to the true conductivity and standard deviation = 0.1. Here are six measurements on the same standard iron rod, which is supposed to have conductivity 10.1. 10.08 9.89 10.04 10.15 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.) blank - blank. microsiemens per centimeter

Explanation / Answer

Please Note: Number of measurements given is 7.

Given that = 0.1, n = 7, = 0.1

From the data x = 10.083

Since population standard deviation is known but n < 30, the tcritical (2 tail) for = 0.1, for df = n -1 = 6, is 1.9432

The Confidence Interval is given by x ± ME, where

ME = Zcritical * rac{s}{sqrt{n}} = 1.9432 * rac{0.1}{sqrt{7}} = 0.073

The Lower Limit = 10.083 - 0.073 = 10.010

The Upper Limit = 10.083 + 0.073 = 10.156

The Confidence Interval is (10.010 , 10.156)

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