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? Explain.

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::

Correct option: (3)

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

Explanation:
Since the population standard deviation is known, z - test is appropriate even though sample Size = n = 8 < 30, Small Sample.

Since the engineer adpted biased way of taking the first 8 screws from the batch and weighing them, which is a Convenience Sampling and is not Simple Random Sampling.

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