Question

leah is president of her schools chess club. she wants to choose 12 members of the club to take a survey. leah writes the name of each club member on a card. she shuffles the cards and chooses 12 cards without looking. is this sample likely to be representative of the population? yes, because each club member has an equal chance of being chosen. yes, because the chosen club members are part of the population. no, because some club members will not be chosen. no, because the chosen club members are not part of the population.

Explanation:

A representative sample should give each member of the population an equal chance of being selected. Here, Leah is using a random sampling method (shuffling cards and choosing without looking). In random sampling, if each element (club member) has an equal probability of being chosen, the sample is likely to be representative.

• The second option “Yes, because the chosen club members are part of the population” is too vague. Just being part of the population doesn't guarantee representativeness.
• The third option “No, because some club members will not be chosen” is incorrect. In any sample (unless it's a census), some members won't be chosen, but that doesn't mean the sample isn't representative.
• The fourth option “No, because the chosen club members are not part of the population” is wrong as the chosen members are from the club (the population in question).

Answer:

Yes, because each club member has an equal chance of being chosen.