Question

several members of a running club would like to survey the rest of the members to determine which 5k race the club should enter. they decide to sample 10 of the 78 members and have them fill out a survey about their race preference. which of the following would be a simple random sample?
write each members name on an equal - sized slip of paper. place the slips of paper in a bag and shake. draw 10 slips of paper and survey the members selected.
write each members name on an equal - sized slip of paper. place the slips of paper in a bag. draw 10 slips of paper off the top and survey the members selected.
write each members name on a scrap of paper. fold the pieces of paper and place them in a bag. draw 10 slips of paper off the top and survey the members selected.
write each members name on a scrap of paper. fold the pieces of paper, place them in a bag, and shake the bag. draw 10 slips of paper and survey the members selected.

Explanation:

A simple random sample requires that each member has an equal chance of being selected. In the first option, writing each member's name on an equal - sized slip of paper, placing them in a bag, shaking (to randomize), and then drawing 10 slips gives every member an equal probability of being chosen. The second and third options do not shake the bag, which may lead to a non - random selection (e.g., slips on the top may be from a particular subgroup if not mixed). The fourth option uses "scrap of paper" instead of "equal - sized slip of paper", which could introduce bias (unequal size might make some slips more or less likely to be drawn).

Answer:

Write each member’s name on an equal - sized slip of paper. Place the slips of paper in a bag and shake. Draw 10 slips of paper and survey the members selected.