Probabilistic Systems I The flow of heat in metal bars was first studied analyti

Question

Probabilistic Systems I The flow of heat in metal bars was first studied analytically by the French mathematician Jean Fourier in 1816. The theoretical relationship between heat flux and temperature gradient for homogeneous materials is well known and described by a Fourier equation. However, this relationship does not hold for non-homogeneous materials such as porous-capillary bodies, cellular systems, suspensions, and pastes where heat capacity and its temperature variation depend on differences in energy levels for the atoms (available quantum states). An article in the Journal of Heat Transfer describes an experiment conducted to estimate the mean thermal relaxation lime (defined as the mean time needed for accumulating the thermal energy required for propagative transfer of heat) for several non-homogeneous materials including sand A sample size of n = 16 was used as a basis for calculating a 95% two-sided Cl for true mean thermal relaxation time of sand and the resulting interval was found lobe 20.0 plusminus 6.393 seconds. You decide that a confidence level of 90% is more suitable for decision making when employing sand designs than the 95% level put forth in this article; so using the information presented from this article, find the 90% two-sided Cl for the true mean thermal relaxation time of sand.

Explanation / Answer

n=16

95% CI = 20 +/- 6.393

Therefore , Margin Of error = 6.393

Mean = 20

Margin of error = z*SD/sqrt(n)

=> 6.393 = 1.96 * SD/sqrt(16)

=> SD = (6.393*4)/1.96 = 13.05

Therefore for 90% CI,

New Margin of error = 1.645 * 13.05/sqrt(16) = 5.367

Therefore, 90% CI = (20 - 5.367 , 20 + 5.367)

= ( 14.633 , 25.367) Answer

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