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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