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 a liquid whose electrical conductivity is supposed to be 5. (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 liquid has the Normal distribution with mean μμ equal to the true conductivity and standard deviation σσ = 0.2. Here are 6 measurements on the 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 95% confidence interval for its true conductivity. What is this interval?

Answer 1

Answer :

Given data is :

standard deviation σ = 0.2

Sample size n = 6

5.32 , 4.88 , 5.10 , 4.73 , 5.15 , 4.75

mean = (5.32 + 4.88 + 5.10 + 4.73 + 5.15 + 4.75) / 6

= 29.93 / 6

= 4.988

mean = 4.988

Given confidence interval = 95%

Z value at 1.96

therefore,

CI =

Substitute all values in above formula,

=

=

=

=

=

=

CI = (4.8281 , 5.1479)

therefore,

Confidence interval at 95% using normal distribution is 4.8281 < < 5.1479