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 12% 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

Solution:

a)Note that              
              
p^ = point estimate of the population proportion = x / n =    0.1          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p^ (1 - p^) / n] =    0.021213203          
              
Now, for the critical z,              
alpha/2 =   0.05          
Thus, z(alpha/2) =    1.644853627          
Thus,              
Margin of error = z(alpha/2)*sp =    0.034892615          
lower bound = p^ - z(alpha/2) * sp =   0.065107385          
upper bound = p^ + z(alpha/2) * sp =    0.134892615          
              
Thus, the confidence interval is              
              
(   0.065107385   ,   0.134892615   ) [ANSWER]

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b)

As 93% of 200 are completed, then

x = n p^ = 200*0.93 = 186 [ANSWER]

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c)

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.93      
p2 = x2/n2 =    0.1      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.027847801      
              
          
For the   90%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.05      
z(alpha/2) =    1.644853627      
Margin of error = z(alpha/2)*sd =    0.045805556      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    0.784194444      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.875805556      
          
Thus, the confidence interval is          
          
(   0.784194444   ,   0.875805556 ) [ANSWER, PROPORTIONS]

(   78.4194444%   ,   87.5805556% ) [ANSWER, PERCENTS]

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