Question 7.3: Coalminers’ Employment Period Study A human resources direct......
Employment Period Study
A human resources director at the Chamber of Mines wishes to estimate the true mean employment period of all coalminers. From a random sample of 144 coalminers’ records, the sample mean employment period was found to be 88.4 months. The population standard deviation is assumed to be 21.5 months and normally distributed.
Find the 95% confidence interval estimate for the actual mean employment period (in months) for all miners employed in coal mines.
Given \bar{x} = 88.4 months, \sigma = 21.5 months and n = 144 miners.
- Find the standard error of the sample mean.
\sigma_{\bar{x}}=\frac{\sigma }{\sqrt{n} }=\frac{21.5}{\sqrt{144} } = 1.792 months
- From the z-table, the 95% confidence level equates to z-limits of ±1.96.
- Compute the margin of error = 1.96 × 1.792 = 3.51
- Thus the lower limit is: 88.4 – 1.96(1.792) = 88.4 – 3.51 = 84.89 months
and the upper limit is: 88.4 + 1.96(1.792) = 88.4 + 3.51 = 91.91 months.
Thus the 95% confidence interval is defined as 84.89 ≤ μ ≤ 91.91 months.
Management Interpretation
There is a 95% chance that the average employment period of all coalminers lies between 84.89 and 91.91 months.