Question

Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that σ = 4 psi. A random sample of 8 specimens is tested, and the average breaking strength is found to be 98 psi. Find a 95% two-sided confidence interval on the true mean breaking strength. Round the answers to 1 decimal place.

Answer 1

Answer:
`(95.2,\ 100.8)`

Explanation:

Given : Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that σ = 4 psi.

A random sample of 8 specimens is tested, and the average breaking strength is found to be 98 psi.

i.e. n= 8 and
`\overline{x}=98`

Critical value for 95% confidence =
`z_(\alpha/2)=1.96`

Confidence interval for population mean :-

`\overline{x}\pm z_(\alpha/2)(\sigma)/(√(n))`

i.e.
`98\pm (1.96)(4)/(√(8))`

`\approx98\pm 2.7719`

`=(98-2.7719,\ 98+2.7719)`

`=(95.2281,\ 100.7719)\approx(95.2,\ 100.8)`

Hence, a 95% two-sided confidence interval on the true mean breaking strength. =
`(95.2,\ 100.8)`