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 teacher’s claim is true, 100 simulated proportions are displayed in the dotplot.

simulated proportion of red marbles
dotplot image with proportion of red marbles on the x - axis from 0.35 to 0.75

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 10 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 18 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 only \(10\) 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.