Question

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that σ = 3 psi. A random sample of 10 specimens is tested, and the average breaking strength is found to be 94 psi. Find a 95% two-sided confidence interval on the true mean breaking strength. Round the answers to 1 decimal place

Answer 1

95% Confidence interval: (92.1,95.9)

Explanation:

We are given the following in the question:

Sample mean,
`\bar{x}` = 94 psi

Sample size, n = 10

Alpha, α = 0.05

Population standard deviation, σ = 3 psi

95% Confidence interval:

`\mu \pm z_(critical)(\sigma)/(√(n))`

Putting the values, we get,

`z_(critical)\text{ at}~\alpha_(0.05) = 1.96`

`94 \pm 1.96((3)/(√(10)) ) \\\\= 94 \pm 1.86 \\\\= (92.14,95.86)\approx (92.1,95.9)`

(92.1,95.9) is the required 95% confidence interval on the true mean breaking strength.