The Ping Company makes custom built golf clubs and competes in the 84 billion go
ID: 3266719 • Letter: T
Question
The Ping Company makes custom built golf clubs and competes in the 84 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 book to repair golf clubs to the company by mall determined at 17% 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, 94% of orders were complicated within 5 days. Assume that each of the estimated percents is based on a random sample of 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. () (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. () (c) Give a 90% confidence interval for the improvement. Express this both for a difference in proportions and parents, and for a difference in percents. (Define the groups so that the difference will be proportions () positive. Round your answers for proportion to three decimal places and answers for percents to one decimal places.) percents ()Explanation / Answer
Solution
Number of orders completed before change within 5 days = 200 x 0.17 (17%) = 34 ANSWER
90% confidence interval for proportion of orders completed within 5 days before change
= pcap ± Z/2[sq.rt{pcap(1 – pcap)/n}], where pcap = sample proportion (0.17 or 17%),
n = sample size (200) and Z/2 = upper 2.5% point of N(0, 1) = 1.645 [using Excel Function]
= 0.17 ± 1.645[sq.rt{0.17 x 0.83)/200}] = 0.17 ± 0.0437 = (0.126, 0.214) ANSWER
Number of orders completed after change within 5 days = 200 x 0.94 (94%) = 188 ANSWER
90% confidence interval for proportion of orders completed within 5 days after change
= pcap ± Z/2[sq.rt{pcap(1 – pcap)/n}], where pcap = sample proportion (0.94 or 94%),
n = sample size (200) and Z/2 = upper 2.5% point of N(0, 1) = 1.645 [using Excel Function]
= 0.94 ± 1.645[sq.rt{0.94 x 0.06)/200}] = 0.94 ± 0.0276 = (0.912, 0.968) ANSWER
90% confidence interval for improvement in proportion of orders completed within 5 days due to change
If p1 and p2 are proportion of orders completed within 5 days before and after change respectively, we want 90% confidence interval for (p2 – p1), which is given by:
(p2cap – p1cap) ± Z/2[sq.rtpcap(1 – pcap){(1/n1) + (1/n2)}], where p2cap and p1cap are respectively sample proportion of orders completed within 5 days after and before change,
pcap = (n1p1cap + n2p2cap)/(n1 + n2); n1 and n2 are the two sample sizes (200 each), and Z/2 = upper 2.5% point of N(0, 1) = 1.645 [using Excel Function]
= (0.94 – 0.17) ± 1.645[sq.rt{0.555 x 0.445 x (2/200)}] = 0.77 ± 0.0818
= (0.688, 852) ANSWER
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