Question

as part of a statistics project, a teacher brings a bag of marbles containing 600 white marbles and 200 red marbles. she tells the students the bag contains 800 total marbles, and asks her students to determine how many red marbles are in the bag without counting them.
a student randomly draws 150 marbles from the bag. of the 150 marbles, 41 are red.
the data - collection method can best be described as
survey
experiment
observational study
census
the target population consists of
the 800 marbles in the bag
the 41 red marbles drawn by the student
the 200 red marbles in the bag
the 150 marbles drawn by the student
none of the above
the sample consists of
the 800 marbles in the bag
the 200 red marbles in the bag
the 150 marbles drawn by the student
the 41 red marbles drawn by the student
none of the above
based on the sample, the student would estimate that marbles in the bag were red.

Explanation:

1. For the data - collection method: An observational study involves observing and measuring characteristics of a sample without trying to influence the outcome. Here, the student is just drawing marbles and observing the number of red ones, not manipulating any variables. A survey involves asking questions, an experiment involves treatment and control groups with manipulation, and a census is a count of the entire population.
2. The target population is the entire group of interest. Here, the goal is to know about the marbles in the bag, so the 800 marbles in the bag is the target population.
3. The sample is the subset of the population that is actually observed or measured. The 150 marbles drawn by the student is the sample.
4. To estimate the number of red marbles in the bag based on the sample, we set up a proportion. Let \(x\) be the number of red marbles in the bag. The proportion is \(\frac{41}{150}=\frac{x}{800}\), and solving for \(x\) gives \(x=\frac{41\times800}{150}\approx219\).

Answer:

1. Observational Study
2. The 800 marbles in the bag
3. The 150 marbles drawn by the student
4. 219