The tutor continues with the part life example, this time offering a two-sided confidence interval.

In my previous post I gave the premise of a part whose mean life (μ) is 36 months, with standard deviation (σ) 10 months. I went on to give a one-sided 95% confidence interval for its minimum life expectancy.

Today, I’ll give a two-sided 95% confidence interval for the part’s expected life. From the normal distribution table, we see that 97.5% of the distribution is less than
μ + 1.96σ. By symmetry, 97.5% will also be greater than μ – 1.96σ. Therefore, the interval from μ – 1.96σ to μ + 1.96σ covers the middle 95% of the distribution, since it excludes both the top and bottom 2.5%.

In our case, μ=36, while σ=10. The two-sided interval is 36-1.96(10) to 36+1.96(10), or 16.4 to 55.6 months. 95% of the time, the part will last between 16.4 months and 55.6 months.

Compared to the one-sided interval of the previous post (which was ≥19.55), the two-sided interval is more permissive on the low end (at 16.4). However, it’s less permissive on the top end (55.6); the one-sided interval makes no estimate of top end life.

I’ll be talking more about confidence intervals.

Source:

Harnett, Donald L. and James L. Murphy. Statistical Analysis for Business and
   Economics. Don Mills: Addison-Wesley, 1993.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.