Question

A manufacturing process sometimes has a fault which causes the mean weight of a screw to be lower than it should be, the fault does not affect the standard deviation of the produced screws, which is known for the population. An engineer wants to test whether the fault is present and conducts a z-test for means on the screw weights by taking the first 8 screws from the batch and weighing them. Which of the following best describes the appropriateness of this test?

My Thoughts- Doesn't a Z-test for means require that the sample be >30? Also does it need to be a simple random sample for a Z-test for means, but only one answer is appropriate.

Group of answer choices

A z-test for means is inappropriate because the sample size is too small.

The chance of a type I error is too high because the sample size is too small.

There is likely bias in the sample because the engineer took the first 8 screws rather than taking a simple random sample.

There is no problem with this testing procedure.

Answer #1

**ANSWER::**

Here, the standard deviation is known ( fixed )

and sample size is 8

hence we can use z-test

Since sigma is known the small sample does not affect the use of Z distribution

Also, the sample is independent

**ANS::** **There is
no problem with this testing procedure.**

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A manufacturing process sometimes has a fault which causes the
mean weight of a screw to be lower than it should be, the fault
does not affect the standard deviation of the produced screws,
which is known for the population. An engineer wants to test
whether the fault is present and conducts a z-test for means on the
screw weights by taking the first 8 screws from the batch and
weighing them. Which of the following best describes the
appropriateness...

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