How many observations should a stopwatch time-study analyst plan for in a task that has a standard deviation of 1.47 minutes per piece if the goal is to estimate the mean time per piece to within 0.4 minute with a confidence of 99.0 percent? (Round the intermediate calculations to 2 decimal places. Round the final answer to the next whole number.)
Question
How many observations should a stopwatch time-study analyst plan for in a task that has a standard deviation of 1.47 minutes per piece if the goal is to estimate the mean time per piece to within 0.4 minute with a confidence of 99.0 percent? (Round the intermediate calculations to 2 decimal places. Round the final answer to the next whole number.)
Solution
To answer this question, we need to use the formula for the sample size in a confidence interval estimation, which is:
n = (Z*σ/E)^2
where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level
- σ is the standard deviation
- E is the desired margin of error
Given in the problem, we have:
- σ = 1.47 minutes per piece
- E = 0.4 minute
- The confidence level is 99.0 percent, which corresponds to a Z-score of 2.576 (you can find this value in a standard Z-score table or use a calculator that provides this value).
Substituting these values into the formula, we get:
n = (2.576*1.47/0.4)^2
First, calculate the value inside the parentheses:
= (3.7872)^2
Then, square this value to find the sample size:
= 14.32
Since we can't have a fraction of an observation, we round this up to the next whole number. So, the analyst should plan for 15 observations.
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