A teacher has two large containers filled with blue, red, and green beads, and claims the proportion of red beads are the same in each container. The students believe the proportions are different. Each student 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’s samples contained 10 red beads from the first container and 16 red beads from the second container. Let p1 = the true proportion of red beads in container 1 and p2= the true proportion of red beads in container 2. Which of the following is the correct name for this test?
The student is comparing the proportions of red beads in two separate containers, so the test concerns two population proportions, p1 and p2. The appropriate procedure is a two-proportion z-test; t-tests are used for comparing means, not proportions. Therefore, the correct choice is “two-proportion z-test.”
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