time 12 minutes OPEN aoon-OPEN NOTES ME 42-work systems spring 2016 determine th

Question

time 12 minutes OPEN aoon-OPEN NOTES ME 42-work systems spring 2016 determine the percentage of ide time of the automatic screw machines out of 100 observasons made in a pilot stady, observations showed the machines to be idle 0433 l oo 2. For a confidence of as%. what sthe tarwidth of the proponon in the pilot study? cade your answer 3. How many more observations are needed fan absolute error (half width) of t5% and a confidence level ot of idle sme are dosiad? o a 5) Extra credit. How many more observations are needed a confidence level of 90% in the proponion of idle time is desired instead (use the same hat width of 5%)?

Explanation / Answer

1) here point estimate p=25/100=0.25

and std error =(p(1-p)/n)1/2 =0.0433

for 95% CI, z-1.96

hecen confidence interval =sample proportion -/+ z*std error =0.1651 ; 0.3349

2) half width =z*std error =0.025*1.96 =0.0849

3)here margin of error =half width E =0.05

and z=1.96

p=0.25

hence sample size =p(1-p)*(Z/E)2 =~289 (rounding it up)

hence 189 more observations needed

4) for 90% CI, z=1.2816

hence sample size =~203

hence 103 more observations required

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