Question

A process capability study is conducted for an injection mold. You are tasked to evaluate if the process will yield a greater than 99% acceptance relative to the critical dimension assigned to you. The part requires 1.45” +/-0.008 and you are given 20 parts that measure an average of 1.45” with a standard deviation of 0.0015. What is the range of the true mean with 99% confidence interval?

Answer 1

Answer: 1.4494 and 1.4506

Step-by-step explanation:

Given : Sample size : $n=20$, which is less than 30 so the sample is a small sample.

Sample mean : $\overline{x}=1.45$

Standard deviation : $\sigma= 0.0015$

Significance level :$\alpha=1-0.99=0.01$

Critical value : $t_{n-1,\alpha/2}=t_{19,0.005}=1.729$

The confidence interval for population mean is given by :-

$\mu\ \pm t_{n-1,\alpha/2}\dfrac{\sigma}{\sqrt{n}}$

$=1.45\pm(1.729)\dfrac{0.0015}{\sqrt{20}}\\\\\approx1.45\pm0.0006\\\\=(1.45-0.0006,\ 1.45+0.0006)=(1.4494,\ 1.4506)$

Hence, the range of the true mean with 99% confidence interval is between 1.4494 and 1.4506.