Question

A Brinell hardness test involves measuring the diameter of the indentation made when a hardened steel ball is pressed into material under a standard test load. Suppose that the Brinell hardness is determined for each specimen in a sample of size 32, resulting in a sample mean hardness of 64.3 and a sample standard deviation of 6.0. Calculate a 99% lower confidence bound for true average Brinell hardness for material specimens of this type.

Answer 1

Answer:

61.57

Step-by-step explanation:

Sample size (n) = 32

Sample mean hardness (X) = 64.3

Sample standard deviation (s) = 6.0

Z-score for a 99% confidence interval (Z) = 2.576

The lower confidence bound (L) for a confidence interval is determined by the following expression

$L= X - Z*\frac{s}{\sqrt{n} }$

Applying the given data:

$L=64.3 - 2.576*\frac{6.0}{\sqrt{32}}\\L=61.57$

For the given material, the lower confidence bound for true average Brinell hardness is 61.57.