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 15% 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, 87% 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? 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? 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 completed in 5 days or less before the changes = 200(0.15) = 30

The statistical software output for 90% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:

Hence.

90% confidence interval for the proportion of orders will be:

(0.108, 0.192)

b) Number of orders completed in 5 days or less after the changes = 200(0.87) = 174

The statistical software output for 90% confidence interval is:

One sample proportion confidence interval:
p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:

Hence,

90% confidence interval for the proportion of orders will be:

(0.831, 0.909)

c) Software output for the improvement:

Two sample proportion confidence interval:
p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions

90% confidence interval results:

Hence,

90% confidence interval for the improvement will be:

Proportions: (0.663, 0.777)

Percentage: (66.3%, 77.7%)

Proportion Count Total Sample Prop. Std. Err. L. Limit U. Limit p 30 200 0.15 0.025248762 0.10846948 0.19153052

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