You’re an operations engineer working for a shipping company, and you’re interes
ID: 3178383 • Letter: Y
Question
You’re an operations engineer working for a shipping company, and you’re interested in the timeliness of shipments made by the company. You look back on a sample of historical data of shipments falling into five categories: More than 3 days early, Between 0 and 3 days early, On time, Between 0 and 3 days late, More than 3 days late. The counts of shipments falling into these five categories are found below. Find a 95% confidence interval for the true proportion of late shipments.
Shipment category
Count
More than 3 days early
87
Between 0 and 3 days early
156
On time
419
Between 0 and 3 days late
201
More than 3 days late
118
Shipment category
Count
More than 3 days early
87
Between 0 and 3 days early
156
On time
419
Between 0 and 3 days late
201
More than 3 days late
118
Explanation / Answer
total sample size n=981
out of which 319 are delayed
hence mean proportion p =319/981=0.325
for std error =(p(1-p)/n)1/2 =0.015
for 95% CI, z=1.96
hence confidence interval =mean +/- z*std error =0.2959 ; 0.3545
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