Random samples of size n 320 are taken from a population with p 0.08 a. Calculat

Question

Random samples of size n 320 are taken from a population with p 0.08 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 centerline, the upper control limit (UCL), and the lower control limit (LCL) for the P chart if samples of 200 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 size - References eBook &Resources; Worksheet Difficulty: 3 Hard Learning Objective: 07-07

Explanation / Answer

A) here central line is p=0.08

Error of Control line is E1=0.016 for 300 samples

So UCL=0.08-0.016=0.064

LCL=0.08+0.016=0.096

B) for n=200

Error is E2=0.019

So UCL=0.08-0.019=0.061

LCL=0.08+0.019=0.099

C) It can be noted that the interval length in n=200 is more wider than the n=300. That is because in taking more samples we get better and precise estimates where actually value of P should lies. So control limits have larger sample size in smaller samples.

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