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, randomly selects 50 beads, counts the number of red beads, and returns the beads to the container. The student repeats this process for the second container.

One student sampled 13 red beads from the first container and 16 red beads from the second container.

Assuming the conditions for inference are met, what is the 95% confidence interval for the difference in proportions of red beads in each container?

Answer: Assuming the conditions for inference are met, we can use the difference in proportions of red beads in the two samples to estimate the difference in proportions of red beads in the population. The 95% confidence interval for the difference in proportions of red beads in the two containers is calculated as follows:

Difference in sample proportions = p1 - p2 = (13/50) - (16/50) = -0.03

Standard error of the difference in sample proportions = sqrt{(p1*(1-p1)/n1) + (p2*(1-p2)/n2)} = sqrt{(13/50)(37/50)/50 + (16/50)(34/50)/50} = 0.079

Margin of error = z* * standard error of the difference in sample proportions = 1.96 * 0.079 = 0.155

95% Confidence interval for the difference in proportions of red beads in the two containers = (difference in sample proportions - margin of error, difference in sample proportions + margin of error) = (-0.03 - 0.155, -0.03 + 0.155) = (-0.185, 0.125)

So, we can be 95% confident that the difference in the proportion of red beads in the two containers is between -0.185 and 0.125.

Step-by-step explanation: