A teacher has a large container of blue, red, and green beads. She wants her students to estimate the proportion of red beads. Each student selects 50 beads, counts the number of red beads, and returns the beads to the container. One student sample has 15 red beads. The students are asked to construct a 95% confidence interval for the true proportion of red beads in the container. Are the conditions for inference met?
Answer
A
Yes, the conditions for inference are met.
B
No, the 10% condition is not met.
C
No, the randomness condition is not met.
D
No, the Large Counts Condition is not met.
Explanation
A confidence interval requires a random sample or a random selection process, but the question only says that the student selects beads; it does not say the selection is random. Returning the beads helps satisfy the independence condition, and the sample has 15 red beads and 35 non-red beads, so both counts are at least 10. The randomness condition is not established, so the conditions are not all met.
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