. Data from an 8 hour work sampling are shown below: (15 points) 27 Running Idle

Question

. Data from an 8 hour work sampling are shown below: (15 points) 27 Running Idle- maintenance Idle- waiting to be11 unloaded Idle- Other (a) what % of the time was the machine running? (b) what % of the time was the machine waiting to be unloaded? (c) What is the limit of accuracy of this study (with regard to the machine running) for -06? (d) What is the 95% confidence interval for the machine running? (e) Your manager says the range in part d is unacceptably large. She would like to narrow the range down to ± 1 minute of running time. How many observations should you collect to achieve this?

Explanation / Answer

(a) % of the time machine running = 27/50 = 54%

(b) % of the time machine waiting to be unloaded = 11/50 = 22%

(c)

Proportion of machine running, p = 27/50 = 0.54

= 0.06

Z/2 = 2.88

Limit of accuracy = Z/2(p(1-p)/n) = 0.20305

(d) For 95% confidence, Z/2 = 2.96

Using formula, E = Z/2(p(1-p)/n), substituting values of E = 0.20305, n=50 and Z/2 = 2.96, we get, p = 0.621

Lower limit of 95% confidence interval = (1-0.621)*50 = 0.379*50 = 19

Upper limit of 95% confidence interval = 0.621*50 = 31

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