The Ping Company makes custom-built golf clubs and competes in the $4 billion go

Question

The Ping Company makes custom-built golf clubs and competes in the $4 billion golf equipment industry. To improve its business processes, Ping decided to seek ISO 9001 certification. As part of this process, a study of the time it took to repair golf clubs sent to the company by mail determined that 14% of orders were sent back to the customers in 5 days or less. Ping examined the processing of repair orders and made changes. Following the changes, 88% of orders were completed within 5 days. Assume that each of the estimated percents is based on a random sample of 200 orders.

(a) How many orders were completed in 5 days or less before the changes?
orders

Give a 90% confidence interval for the proportion of orders completed in this time. (Round your answers to three decimal places.)

  ,

(b) How many orders were completed in 5 days or less after the changes?
orders

Give a 90% confidence interval for the proportion of orders completed in this time. (Round your answers to three decimal places.)

  ,

(c) Give a 90% confidence interval for the improvement. Express this both for a difference in proportions and for a difference in percents. (Define the groups so that the difference will be positive. Round your answers for proportions to three decimal places and round your answers for percents to one decimal place.)

Explanation / Answer

a) number of orders =np=0.14*200=28

for before implementation: p=0.14

hence std error=(p(1-p)/n)1/2=0.0245

for 90% CI, z =1.6449

hence confidence interval =p +/- z*std error =(0.0996 ; 0.1804)

b) after change number of orders =0.88*200=176

p=0.88

std error=0.023

confidence interval =p +/- z*std error =(0.8422 ; 0.9178)

c) p1=0.88 ; p2=0.14

for difference std error =(p1(1-p1)/n1+p2(1-p2)/n2)1/2 =0.0336

hence confidence interval in proportion =(p1-p2) +/- z*std error =0.6847 ; 0.7953

confidence interval in percentage =68.47 ; 79.53

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