Question

a large bakery produces cakes in an assembly line. sergio noticed a potential defect that seems to be showing in every other cake. he decides that in the next production run, hell take a random sample of cakes to get a better idea of how many cakes might have this defect. why might sergio choose a simple random sample instead of a systematic random sample? choose all answers that apply: a if the defect is in every other cake, a systematic random sample could miss it completely depending on what sergio chooses for k. b a simple random sample can save time since it is less involved than a systematic random sample. c a simple random sample guarantees that sergio will get some cakes from each hour of production.

Explanation:

In systematic random sampling, if the defect occurs in a periodic pattern (every other cake here), the sampling interval ($k$) could be set in a way that the defect is missed. Simple random sampling has no such risk related to a fixed - interval pattern. Also, simple random sampling is generally less complex and can save time compared to systematic random sampling which requires setting up a sampling interval. There is no guarantee in simple random sampling that cakes from each hour of production will be selected.

Answer:

A. If the defect is in every other cake, a systematic random sample could miss it completely depending on what Sergio chooses for $k$.
B. A simple random sample can save time since it is less involved than a systematic random sample.