7. Quality Control Production managers on an assembly line must monitor the outp

Question

7. Quality Control Production managers on an assembly line must monitor the output to be sure that the level defective products remains small. They periodically inspect a random sample of the items pr they find a significant increase in the proportion of items that must be rejected, they will halt assembly process until the problem can be identified and repaired. oduced. if the a. Write the hypotheses b. In this context, what is a Type I error? c. In this context, what is a Type Il error? d. Which type of error would the factory owner consider more serious? e. Which type of error might customers consider more serious? Explain.

Explanation / Answer

a)

H0: There is a significant increase in the proportion of defective samples

H1: There is no significant increase in the proportion of defective samples

b) Type-1 Error:

Rejecting H0 when it is true

Meaning that we are not stopping the assembly line even after finding a significant increase in the proportion of the defective samples.

The consequence is that there will be many defective samples in the lot produced

c) Type-2 Error:

Not rejecting H0 when it is false

Meaning that we are stopping the assembly line even after finding no significant increase in the proportion of the defective samples.

The consequence is that there will be a shortage in the production

d) For the factory owner, Type-2 error would be more serious because his top-line will come down due to low production and that hits the margin

The customer will not be hurt because he can buy the products from another supplier if output from this particular firm is low

e) For the customer, Type-1 error is more serious as he cannot afford to have defective products in the lot that he purchased

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