Question

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 shakes the first container, 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 contain 13 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. The p-value for this significance test is 0.171. Which of the following is the correct conclusion for this test of the hypotheses level?

1) Reject the null hypothesis and conclude that the proportions of red beads are different in the two containers
2) Fail to reject the null hypothesis and conclude that the proportions of red beads are the same in the two containers
3) Cannot be determined based on the given information
4) None of the above

Answer 1

The correct conclusion is to fail to reject the null hypothesis and conclude that the proportions of red beads are the same in the two containers.

Step-by-step explanation:

The correct conclusion for this test of the hypotheses level is option 2) Fail to reject the null hypothesis and conclude that the proportions of red beads are the same in the two containers.

To determine the correct conclusion, we need to compare the p-value for the test to the significance level, which is 0.05.

Since the p-value (0.171) is greater than the significance level (0.05), we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that the proportions of red beads are different in the two containers.