Question

a teacher tells her students that a large jar of marbles contains 55% red marbles. students randomly select a sample of 40 marbles and determined the proportion of red marbles. one sample contained 18 red marbles. assuming the teachers claim is true, 100 simulated proportions are displayed in the dotplot.

simulated proportion of red marbles
dotplot image

using the dotplot and sample proportion, is there convincing evidence that the teacher’s claim is false?

yes, because a proportion of 0.45 or more occurred 87 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
yes, because a proportion of 0.45 or less occurred only 16 out of 100 times, the sample proportion of red marbles is statistically significant and there is convincing evidence that the teacher’s claim is false.
no, because a proportion of 0.45 or more occurred 87 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.
no, because a proportion of 0.45 or less occurred 16 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher’s claim is false.

Explanation:

Answer:

No, because a proportion of 0.45 or less occurred 16 out of 100 times, the sample proportion of red marbles is not statistically significant and there is not convincing evidence that the teacher's claim is false.