http://eato 2 Chapter 7 Homeworkx ? Amazon.com-Online S.- ? CengageNowv2 Onlinet
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Question
http://eato 2 Chapter 7 Homeworkx ? Amazon.com-Online S.- ? CengageNowv2 Onlinet TripAdvesor 5· 9.00 points Random samples of size n 410 are taken from a population with p 0.09 a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the P chart Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.) Centerline Upper Control Limit Lower Control Limit b. Calculate the centerine, the upper control limit (UCL), and the lower control limit (LCL) for the chart samples of 290 are used. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.) Centerline Upper Control Limit Lower Control Limit c. Discuss the effect of the sample size on the control limits The control limits have a (Click to select) spread with smaller sample sizes due to the Click to select) standard error for the smaller sample sizeExplanation / Answer
Solution :
Given that n = 410 and p = 0.09
=> q = 1-p = 0.91
a. centerline = p = 0.09
Upper control limit = p + 3*sqrt(p*q/n)
= 0.09 + 3*sqrt(0.09*0.91/410)
= 0.132
Lower control limit = p - 3*sqrt(p*q/n)
= 0.09 - 3*sqrt(0.09*0.91/410)
= 0.048
b. n = 290 , p = 0.09 , q = 0.91
centerline = 0.09
upper control limit = p + 3*sqrt(p*q/n)
= 0.09 + 3*sqrt(0.09*0.91/290)
= 0.140
Lower control limit = p - 3*sqrt(p*q/n)
= 0.09 - 3*sqrt(0.09*0.91/290)
= 0.040
c. => The control limits have a larger spread with smaller sample sizes due to the increased standard error for the smaller sample size
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