High School

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A teacher has two large containers filled with blue, red, and green beads. He wants his students to estimate the difference in the proportion of red beads in each container. Each student shakes the first container, selects 25 beads, counts the number of red beads, and returns the beads to the container. The students repeat this process for the second container. One student sampled 10 red beads from the first container and 8 red beads from the second container. The students are asked to construct a 95% confidence interval for the difference in proportions of red beads in each container. Are the conditions for inference met?

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.

Answer :

The randomness condition is not met for constructing a confidence interval based on non-random bead sampling.

Question: The students are asked to construct a 95% confidence interval for the difference in proportions of red beads in each container. Are the conditions for inference met?

Answer: No, the randomness condition is not met since students weren't randomly chosen to sample the beads. Therefore, the conditions for inference are not fully met, and caution should be exercised when interpreting the results.

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