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In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made?
- a)0.16, 0.24
- b)0.12, 0.28
- c)0.08, 0.32
- d)None of these
Correct answer is option 'B'. Can you explain this answer?
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In carrying out a work sampling study in a machine shop, it was found ...
Confidence Interval Calculation for Lathe Downtime
Given:
- Lathe downtime = 20%
- Number of observations = 100
- Confidence level = 95%
We can calculate the 95% confidence interval for the estimate of lathe downtime using the following formula:
CI = p ± Zα/2 * sqrt(p(1-p)/n)
Where:
- CI = confidence interval
- p = sample proportion (downtime percentage)
- Zα/2 = Z-score for the desired confidence level (1.96 for 95%)
- n = sample size
Substituting the given values:
CI = 0.2 ± 1.96 * sqrt(0.2(1-0.2)/100)
CI = 0.2 ± 0.04
CI = (0.16, 0.24)
Therefore, the 95% confidence interval for the estimate of lathe downtime is 0.16 to 0.24.
Option B, 0.12 to 0.28, is the closest answer choice to the calculated confidence interval.
Given:
- Lathe downtime = 20%
- Number of observations = 100
- Confidence level = 95%
We can calculate the 95% confidence interval for the estimate of lathe downtime using the following formula:
CI = p ± Zα/2 * sqrt(p(1-p)/n)
Where:
- CI = confidence interval
- p = sample proportion (downtime percentage)
- Zα/2 = Z-score for the desired confidence level (1.96 for 95%)
- n = sample size
Substituting the given values:
CI = 0.2 ± 1.96 * sqrt(0.2(1-0.2)/100)
CI = 0.2 ± 0.04
CI = (0.16, 0.24)
Therefore, the 95% confidence interval for the estimate of lathe downtime is 0.16 to 0.24.
Option B, 0.12 to 0.28, is the closest answer choice to the calculated confidence interval.
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In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made?a)0.16, 0.24b)0.12, 0.28 c)0.08, 0.32d)None of theseCorrect answer is option 'B'. Can you explain this answer?
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