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?