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: $(95.2,\ 100.8)$

Step-by-step 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 :-

$\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

i.e. $98\pm (1.96)\dfrac{4}{\sqrt{8}}$

$\approx98\pm 2.7719$

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

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

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