Question

Defect sampling is used in industrial settings to determine the types and amount of defects in manufactured items. The manager is considering reducing the sampling from 32 items a day to 8 items a day. a) What do you expect to happen to variability in the number of defective items when sampling is reduced? (5 points) b) Compare the histograms below, which shows the distribution of observed defects. Would you recommend a scheme of 1 item inspected per day? Explain why. (10 points) c) The sampling scheme of n=1 per day has a mean of 11.4 and a standard deviation of 2.71. The sampling scheme of 32 per day has a mean of 10.9 and a standard deviation of 0.99. Calculate the standard errors of the schemes. What can you deduce from the standard errors? (10 points) Total: 25 points Sampling scheme n=1 4 6 8 10 12 14 16 18 20 Sampling scheme n=8 4 6 8 10 12 14 16 18 20 Sampling scheme n=32 4 6 8 10 12 14 16 18 20

Answer 1

a)

Variance is inversely proportion to the sample size. Infinite size of a sample would guarantee a perfect estimate of some parameter. As less and less size of sample is considered, the estimate would be far from the true value, thereby increasing the variance.

Hence, the variability in the number of defective items will increase when sampling is reduced.

b)

A sampling scheme of n=1 will cause a high variability in the estimate of the amount of defect as compared to n=32

Hence, scheme of 1 item inspected per day is not recommended.

c)

Standard error is given by

$SE=\frac{\sigma }{\sqrt{n}}$

Standard error of scheme n=1

$n=1=\frac{2.71 }{\sqrt{1}}$

n=1= 2.71

Standard error of scheme n=32

$n=32=\frac{0.99}{\sqrt{32}}$

$n=32=0.175$

The lower standard error for n=32 indicates that the estimate of the amount of defect is closer to the actual amount of defect than in the case of n=1

Since n=32 gives better estimate of the average no. of defects hence we can deduce that the sampling scheme of n=32 should be used.