Question

The diameter of holes for a cable harness is known to have a normal distribution with σ = 0.01 inches. A random sample of size 10 yields an average diameter of 1.5045 inches. Find a 99% two-sided confidence interval on the mean hole diameter. Round the answers to 4 decimal places.

Answer 1

Answer: (1.4964, 1.5126)

Step-by-step explanation:

We know that the confidence interval for population mean is given by :-

$\overline{x}\ \pm z*\dfrac{\sigma}{\sqrt{n}}$

, where ${\sigma$= population standard deviation.

n= sample size

$\overline{x}$ = Sample mean

As per given , we have

σ = 0.01 inches

n= 10

$\overline{x}=1.5045$

Also, the critical value for 99% confidence interval = $z*=2.576$ [From x-value table.]

[Significance level =1-0.99=0.01 and $z_{\alpha/2}\ at\ \alpha=0.01$ is 2.576.]

Then, the 99% two-sided confidence interval on the mean hole diameter will be :-

$1.5045\ \pm (2.576)\dfrac{0.01}{\sqrt{10}}\\\\\approx1.5045\pm(2.576)(0.00316)=1.5045\pm0.00814016=(1.5045-0.00814016,\ 1.5045+0.00814016)\\\\=(1.49635984,\ 1.51264016)\approx(1.4964,\ 1.5126)$

Hence, the required confidence interval = (1.4964, 1.5126)