Question

question #5
a sales representative wishes to survey her client base of 47 companies. she has 47 business cards, all identical size, from her
contacts in the companies, and decides to drop them all in the small box, shake them up, and reach in to pick 5 cards for her sample.
this is an example of:
o simple random sampling
o convenience sampling
o systematic sampling
o cluster sampling
question #6
ten thousand marbles were produced on a production line. the first 100 marbles off the line were taken and tested for roundness.
does this sampling result in a simple random sample?
o no, because each item does not have an equal chance of being selected.
o no, because each group of items does not have an equal chance of being selected
o yes, because each item has an equal chance of being selected.
o yes, because each group of items has an equal chance of being selected.

Explanation:

Question #5

Simple Random Sampling involves selecting a subset of individuals (or in this case, business cards) from a population (47 business cards) where each individual has an equal chance of being selected. Here, all 47 cards are in the box, shaken (to randomize), and 5 are picked. Each card has an equal probability of being chosen.

• Convenience Sampling would be selecting based on ease (e.g., only nearby clients).
• Systematic Sampling would involve a fixed - interval selection (e.g., every \(n^{th}\) card).
• Cluster Sampling would group the population and then select clusters (not the case here).

In a simple random sample, every individual (marble) in the population (10000 marbles) should have an equal chance of being selected. Here, only the first 100 marbles off the line are selected. Marbles produced later (e.g., the 101st - 10000th) have no chance of being in the sample. So, each item does not have an equal chance of being selected.

• The second option about groups is not relevant as the issue is with individual items.
• The 'Yes' options are incorrect because of the unequal chance for all marbles.

Answer:

Simple Random Sampling

Question #6