Question

The breaking strength of yarn used in the manufacture of woven carpet material is Normally distributed with 2.4 psi (pound-force per square inch). A random sample of 16 specimens of yarn from a production run were measured for breaking strength and a confidence interval for the breaking strength of yarn was found to be (128.7, 131.3).

(a) What is the confidence level, C, of this interval?

A. 90% B. 92% C. 95% D. 96% E. 97% F. 98.5% G. 99% H. None of Above

(b) What is the margin-of-error of this study?

A. 130 B. 65 C. 2.6 D. 1.3 E. None of Above F. Unable to determine with the information provided.

(c) Is it possible that the breaking strength of yarn used in the manufacture of woven carpet is 120 psi?

A. Yes B. No C. Unable to determine with the information provided.

Answer 1

Here' the answer to the question. please write back in case you've doubts.

The mean of (128.7, 131.3) is the average of the upper and lower bounds .

So, mean = (128.7 + 131.3)/2 = 130

a.

The margin of error is Upper bound - Mean = 1.3

So, MOE = 1.3

Z*2.4/sqrt(16) = 1.3

Z = 1.3*4/2.4 = 2.1667

Now, to find the what CI is this lets find the cumulative probability for this Z

We can use either Z-tables or NORMSDIST(Z) formula in Excel to convert Z to probability value.

Hence, P(Z<2.1667) = .985

So, the CI is 1-2*(1-.985) % = 97%

E. 97% is correct

b.

Now, the margin of error is Upper bound - Mean = 131.3 - 130 = 1.3,

Hence, D is correct

c.

The possbility is measured by probabability. If probability of 120 psi or below is more than .05 then we can say such an event is "possible"

So, lets calcualte P(X<120) = P(Z< (120-130)/(2.4/sqrt(16)) = P(Z<-16.67) ~ 0.00 , which is less than .05

So, Is it NOT possible that the breaking strength of yarn used in the manufacture of woven carpet is 120 psi

Answer: B. NO