Question

In: Statistics and Probability

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed...

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with σ = 2.4 psi. A random sample of 16 specimens of yarn from a production run was measured for breaking strength, and based on the mean of the sample (x bar), a confidence interval was found to be (128.7, 131.3). What is the confidence level, C, of this interval?

Please show work and explain

A. 0.95

B. 0.99

C. 0.90

D. 0.97

E. it can not be determined with the info provided

Solutions

Expert Solution

Solution :

Given that,

Lower confidence interval = 128.7

Upper confidence interval = 131.3

​  = (Lower confidence interval + Upper confidence interval ) / 2

= (128.7 + 131.3) / 2

= 260 / 2 = 130

= 130

Margin of error = E = Upper confidence interval - ​  = 131.3 - 130 = 1.3

Margin of error = 1.3

E = Z/2* ( /n)

Z/2 = E * n / = 1.3 * 16 / 2.4 = 2.17

Z/2 = 2.17

Z0.015 = 2.17.

/2 = 0.015

= 0.015 * 2 = 0.03

c = 1 - = 1 - 0.03 = 0.97

Confidence level = 0.97

Option D) is correct .

orchestra answered 1 year ago
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