Aquality analyst wants to construct a control chart for determining whether four machines, all producing the same product, are in control with regard to a particular quality attribute. accordingly, she inspected 1,000 units of output from each machine in random samples, with the following results: machine total defectives #1 23 #2 15 #3 29 #4 13 what is the estimate of the standard deviation of the sampling distribution of sample proportions for this process?

Step-by-step explanation:

1) As the sample size is 1,000 and there are 23 defectives in the output of the sample collected from Machine #1, the answer is 23/1000=0.023.

2) Estimate of the process proportion of defectives is the average of the proportion of defectives from all samples. In this case, it is : (23+15+29+13)/{4*(1000)}=80/4000=0.02.

3) Estimate of the Standard Deviation: Let us denote the mean (average) of the proportion of defectives by p. Then, the estimate for the standard deviation is : sqrt{p*(1 - p)/n}. Where n is the sample size. Putting p = 0.02, and n = 1000, we get: σ=0.0044.

4) The control Limits for this case, at Alpha risk of 0.05 (i.e. equivalent to 95% confidence interval), can be found out using the formulas given below:

Lower Control Limit : p - (1.96)*σ = 0.02 - (1.96)*0.0044=0.0113.

& Upper Control Limit: p + (1.96)*σ = 0.02 + (1.96)*0.0044 = 0.0287.

5) The proportion defective in each case is : Machine #1: 0.023; Machine #2: 0.015; Machine# 3: 0.029; Machine# 4: 0.013. For the Lower & Upper control limits of 0.014 & 0.026; It is easy to see that Machines #3 & #4 appear to be out of control.

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step-by-step explanation:

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

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