Final answer:
To estimate the mean time per piece to within 1.1 minutes with a 95.5% confidence level, a time study analyst should plan for 23 observations, rounded up from the calculated sample size of 22.36.
Step-by-step explanation:
To calculate the number of observations a time study analyst should plan for in order to estimate the mean time per piece to within a certain margin of error with a specified confidence level, the formula for the sample size n when estimating a mean can be used:
n = (z * σ / E)^2
Where:
- z is the z-score corresponding to the desired confidence level
- σ (sigma) is the population standard deviation
- E is the desired margin of error
Given that the standard deviation σ is 2.6 minutes, the desired margin of error E is 1.1 minutes, and the desired confidence level is 95.5 percent (which corresponds to a z-score of approximately 2 for the normal distribution), we can plug these values into the formula:
n = (2 * 2.6 / 1.1)^2
Calculating this gives us n = (5.2 / 1.1)^2 ≈ 22.36. Since we cannot have a fraction of an observation, we round up to the next whole number, which gives us 23 observations needed.