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:

• Option A: In systematic - random sampling with a sampling interval \(k\), if the defect pattern aligns in a way that the selected items based on \(k\) skip the defective ones, the defect can be missed. For example, if \(k = 2\) and the defect is in every other cake, it depends on the starting point.
• Option B: Simple random sampling is generally less complex and can be quicker to implement as it doesn't require setting up a sampling interval like in systematic - random sampling.
• Option C: There is no guarantee in simple random sampling that cakes from each hour of production will be selected. It is just a random selection from the entire population.

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.