Homework Clinic
Social Science Clinic => Business => Management => Topic started by: Lisaclaire on Dec 3, 2019
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Question 1
A retail store manager is trying to improve and control the rate at which cashiers sign customers up
for store credit cards. Suppose the manager takes 10 samples, each with 100 observations. P-bar
is found to be .05, and the manager does not want a lower limit below .0064. What z-value would
this imply, and how confident can he be that the true lower limit is greater than or equal to .0064?
Question 2
A retail store manager is trying to improve and control the rate at which cashiers sign customers up
for store credit cards. After posting a p-chart of the store's credit card sign-ups the manager takes
new samples of size 50 three weeks later. He finds that each sample of 50 contained 5 credit card
signups on average. Find p-bar and 99.73% control limits.
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Answer 1
Sigma-p = sqrt ( .05∗(1 - .05)/100) = .0217945. Using the equation that LCL = p-bar-z∗sigma-p gives .0064=.05 - z∗(.0217945). Solving gives z = 2. Using table S6.2 shows that for z = 2 the manager can be 95.45% confident.
Answer 2
P-bar = 5/50 = .1 or 10%. Sigma-p = sqrt(.1(1 - .1)/50) = .042426. z = 3 for the given confidence level. Using the equations for control limits gives
UCL= .1 + 3(.042426) = .22728
LCL= .1 - 3(.042426) = -.02728 and since a control limit cannot be negative round up to 0.
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Thank you