estimating the population proportion using large samples



problem:
Production Engineer is interested to estimate the capacity of the production team to deliver the projects on time in full. To measure this, the production team has selected a random sample of 450 recent jobs in which 395 jobs were delivered on time in full. The production engineer is convinced to estimate the range of future successful jobs with a 98% confidence interval. 

solution: 

#inputs:
suc_jobs = 395/450 # proportion of successfully delivered jobs 
sample_size = 450
alfa = 0.98 #desired confidence interval 

#finding the z-value:
z_vale = qnorm((1- alfa)/2, 
               mean = 0, 
               sd = 1)

#constructing error:
Error = z_vale*sqrt(((1- suc_jobs)*suc_jobs)/sample_size)

#Constructing the interval:
c(suc_jobs + Error, suc_jobs - Error)

conclusion: 
the production can claim 85% - 92% of all jobs will be delivered right on time in full with 98% certainy. 

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