Question

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

A. 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.
B. 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.
C. 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.
D. 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.

Answer 1

The sample proportion of red marbles is statistically significant, providing convincing evidence that the teacher's claim is false.

Step-by-step explanation:

The correct answer is B. 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. In hypothesis testing, the null hypothesis is that the teacher's claim is true, and the alternative hypothesis is that the teacher's claim is false.

The p-value of 0.0165 indicates that the observed sample proportion of red marbles is unlikely to occur if the teacher's claim is true, leading to the rejection of the null hypothesis in favor of the alternative hypothesis. Therefore, there is convincing evidence that the teacher's claim is false.